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Common Core: 6th Grade Math : Grade 6

Study concepts, example questions & explanations for Common Core: 6th Grade Math

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Example Questions

Example Question #22 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between {m} $\displaystyle {m}$ and {n} $\displaystyle {n}$ if $\displaystyle - 14 m - 16 = n$

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -44\\ \hline 5 & -172\\ \hline 7 & -228\\ \hline 13& -396\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -44\\ \hline 5 & -172\\ \hline 7 & -228\\ \hline 13& -396\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -44\\ \hline 5 & -86\\ \hline 7 & -114\\ \hline 13& -198\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -44\\ \hline 5 & -86\\ \hline 7 & -114\\ \hline 13& -198\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -72\\ \hline 7 & -114\\ \hline 9 & -131\\ \hline 12& -174\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -72\\ \hline 7 & -114\\ \hline 9 & -131\\ \hline 12& -174\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -43\\ \hline 5 & -84\\ \hline 7 & -111\\ \hline 13& -194\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -43\\ \hline 5 & -84\\ \hline 7 & -111\\ \hline 13& -194\\ \hline \end{tabular}}$

Correct answer:

Explanation:

In the equation $\displaystyle - 14 m - 16 = n$, {m} $\displaystyle {m}$ is the independent variable and {m} $\displaystyle {m}$ is the dependent variable. This means, as we manipulate {m} $\displaystyle {m}$, {n} $\displaystyle {n}$ will change.

Because we are given tables in our answer choices, we can plug in the given value for {m} $\displaystyle {m}$ from the table and use our equation from the question to see if that equals the value given for {n} $\displaystyle {n}$ in the table.

Let's start by testing values from the following table:

$\displaystyle {-14(2)+-16=-43}$

$\displaystyle {-28+-16=-43}$

${-44\neq -43}$ $\displaystyle {-44\neq -43}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} $\displaystyle {m}$ and {n} $\displaystyle {n}$ if $\displaystyle {- 14 m - 16 = n}$ ; thus, this answer choice is not correct and can be eliminated.

Next, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -16\\ \hline 11 & -340\\ \hline 14 & -424\\ \hline 16& -480\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -16\\ \hline 11 & -340\\ \hline 14 & -424\\ \hline 16& -480\\ \hline \end{tabular}}$

$\displaystyle {-14(0)-16=-16}$

$\displaystyle {0-16=-16}$

$\displaystyle {-16=-16}$

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {-14(11)-16=-340}$

$\displaystyle {-154-16=-340}$

${-170\neq -340}$ $\displaystyle {-170\neq -340}$

$\displaystyle {-14(4)-16=-72}$

$\displaystyle {-56-16=-72}$

$\displaystyle {-72=-72}$

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {-14(7)-16=-114}$

$\displaystyle {-98-16=-114}$

$\displaystyle {-114=-114}$

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {-14(9)-16=-131}$

$\displaystyle {-126-16=-131}$

${-142\neq -131}$ $\displaystyle {-142\neq -131}$

Finally, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -44\\ \hline 6 & -100\\ \hline 7 & -114\\ \hline 14& -212\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -44\\ \hline 6 & -100\\ \hline 7 & -114\\ \hline 14& -212\\ \hline \end{tabular}}$

$\displaystyle {-14(2)-16=-44}$

$\displaystyle {-28-16=-44}$

$\displaystyle {-44=-44}$

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {-14(6)-16=-100}$

$\displaystyle {-84-16=-100}$

$\displaystyle {-100=-100}$

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {-14(7)-16=-114}$

$\displaystyle {-98-16=-114}$

$\displaystyle {-114=-114}$

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {-14(14)-16=-212}$

$\displaystyle {-196+-16=-212}$

$\displaystyle {-212=-212}$

All of these values were correct for our equation; thus, this table is our correct answer.

Report an Error

Example Question #23 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between {m} $\displaystyle {m}$ and {n} $\displaystyle {n}$ if -13 = n $\displaystyle -13 = n$

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & -13\\ \hline 9 & -13\\ \hline 10 & -13\\ \hline 16& -13\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & -13\\ \hline 9 & -13\\ \hline 10 & -13\\ \hline 16& -13\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & -13\\ \hline 9 & -26\\ \hline 10 & -26\\ \hline 16& -26\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & -13\\ \hline 9 & -26\\ \hline 10 & -26\\ \hline 16& -26\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -13\\ \hline 6 & -13\\ \hline 14 & -2\\ \hline 17& -3\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -13\\ \hline 6 & -13\\ \hline 14 & -2\\ \hline 17& -3\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & -12\\ \hline 9 & -11\\ \hline 10 & -10\\ \hline 16& -9\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & -12\\ \hline 9 & -11\\ \hline 10 & -10\\ \hline 16& -9\\ \hline \end{tabular}}$

Correct answer:

Explanation:

In the equation -13 = n $\displaystyle -13 = n$, {m} $\displaystyle {m}$ is the independent variable and {m} $\displaystyle {m}$ is the dependent variable. This means, as we manipulate {m} $\displaystyle {m}$, {n} $\displaystyle {n}$ will change.

Let's start by testing values from the following table:

$\displaystyle {0(3)+-13=-12}$

$\displaystyle {0+-13=-12}$

${-13\neq -12}$ $\displaystyle {-13\neq -12}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} $\displaystyle {m}$ and {n} $\displaystyle {n}$ if $\displaystyle {-13 = n}$ ; thus, this answer choice is not correct and can be eliminated.

Next, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -13\\ \hline 5 & -26\\ \hline 8 & -26\\ \hline 13& -26\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -13\\ \hline 5 & -26\\ \hline 8 & -26\\ \hline 13& -26\\ \hline \end{tabular}}$

$\displaystyle {0(4)-13=-13}$

$\displaystyle {0-13=-13}$

$\displaystyle {-13=-13}$

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {0(5)-13=-26}$

$\displaystyle {0-13=-26}$

${-13\neq -26}$ $\displaystyle {-13\neq -26}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} $\displaystyle {m}$ and {n} $\displaystyle {n}$ if $\displaystyle {-13 = n}$ ; thus, this answer choice is not correct and can be eliminated.

$\displaystyle {0(1)-13=-13}$

$\displaystyle {0-13=-13}$

$\displaystyle {-13=-13}$

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {0(6)-13=-13}$

$\displaystyle {0-13=-13}$

$\displaystyle {-13=-13}$

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {0(14)-13=-2}$

$\displaystyle {0-13=-2}$

${-13\neq -2}$ $\displaystyle {-13\neq -2}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} $\displaystyle {m}$ and {n} $\displaystyle {n}$ if $\displaystyle {-13 = n}$ ; thus, this answer choice is not correct and can be eliminated.

Finally, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & -13\\ \hline 9 & -13\\ \hline 11 & -13\\ \hline 13& -13\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & -13\\ \hline 9 & -13\\ \hline 11 & -13\\ \hline 13& -13\\ \hline \end{tabular}}$

$\displaystyle {0(5)-13=-13}$

$\displaystyle {0-13=-13}$

$\displaystyle {-13=-13}$

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {0(9)-13=-13}$

$\displaystyle {0-13=-13}$

$\displaystyle {-13=-13}$

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {0(11)-13=-13}$

$\displaystyle {0-13=-13}$

$\displaystyle {-13=-13}$

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {0(13)-13=-13}$

$\displaystyle {0+-13=-13}$

$\displaystyle {-13=-13}$

All of these values were correct for our equation; thus, this table is our correct answer.

Report an Error

Example Question #24 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between {m} $\displaystyle {m}$ and {n} $\displaystyle {n}$ if $\displaystyle 14 m + 8 = n$

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 8\\ \hline 6 & 184\\ \hline 12 & 352\\ \hline 19& 548\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 8\\ \hline 6 & 184\\ \hline 12 & 352\\ \hline 19& 548\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 9\\ \hline 6 & 94\\ \hline 12 & 179\\ \hline 19& 278\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 9\\ \hline 6 & 94\\ \hline 12 & 179\\ \hline 19& 278\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 8\\ \hline 6 & 92\\ \hline 12 & 176\\ \hline 19& 274\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 8\\ \hline 6 & 92\\ \hline 12 & 176\\ \hline 19& 274\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 8\\ \hline 8 & 120\\ \hline 10 & 159\\ \hline 11& 172\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 8\\ \hline 8 & 120\\ \hline 10 & 159\\ \hline 11& 172\\ \hline \end{tabular}}$

Correct answer:

Explanation:

In the equation $\displaystyle 14 m + 8 = n$, {m} $\displaystyle {m}$ is the independent variable and {m} $\displaystyle {m}$ is the dependent variable. This means, as we manipulate {m} $\displaystyle {m}$, {n} $\displaystyle {n}$ will change.

Let's start by testing values from the following table:

$\displaystyle {14(0)+8=9}$

{0+8=9} $\displaystyle {0+8=9}$

${8\neq 9}$ $\displaystyle {8\neq 9}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} $\displaystyle {m}$ and {n} $\displaystyle {n}$ if $\displaystyle {14 m + 8 = n}$ ; thus, this answer choice is not correct and can be eliminated.

Next, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 36\\ \hline 5 & 156\\ \hline 17 & 492\\ \hline 19& 548\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 36\\ \hline 5 & 156\\ \hline 17 & 492\\ \hline 19& 548\\ \hline \end{tabular}}$

$\displaystyle {14(2)+8=36}$

$\displaystyle {28+8=36}$

{36=36} $\displaystyle {36=36}$

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {14(5)+8=156}$

$\displaystyle {70+8=156}$

${78\neq 156}$ $\displaystyle {78\neq 156}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} $\displaystyle {m}$ and {n} $\displaystyle {n}$ if $\displaystyle {14 m + 8 = n}$ ; thus, this answer choice is not correct and can be eliminated.

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 8\\ \hline 8 & 120\\ \hline 10 & 159\\ \hline 11& 162\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 8\\ \hline 8 & 120\\ \hline 10 & 159\\ \hline 11& 162\\ \hline \end{tabular}}$

$\displaystyle {14(0)+8=8}$

{0+8=8} $\displaystyle {0+8=8}$

{8=8} $\displaystyle {8=8}$

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {14(8)+8=120}$

$\displaystyle {112+8=120}$

$\displaystyle {120=120}$

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {14(10)+8=159}$

$\displaystyle {140+8=159}$

${148\neq 159}$ $\displaystyle {148\neq 159}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} $\displaystyle {m}$ and {n} $\displaystyle {n}$ if $\displaystyle {14 m + 8 = n}$ ; thus, this answer choice is not correct and can be eliminated.

Finally, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 36\\ \hline 4 & 64\\ \hline 7 & 106\\ \hline 13& 190\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 36\\ \hline 4 & 64\\ \hline 7 & 106\\ \hline 13& 190\\ \hline \end{tabular}}$

$\displaystyle {14(2)+8=36}$

$\displaystyle {28+8=36}$

{36=36} $\displaystyle {36=36}$

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {14(4)+8=64}$

$\displaystyle {56+8=64}$

{64=64} $\displaystyle {64=64}$

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {14(7)+8=106}$

$\displaystyle {98+8=106}$

$\displaystyle {106=106}$

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {14(13)+8=190}$

$\displaystyle {182+8=190}$

$\displaystyle {190=190}$

All of these values were correct for our equation; thus, this table is our correct answer.

Report an Error

Example Question #25 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between {m} $\displaystyle {m}$ and {n} $\displaystyle {n}$ if $\displaystyle - 9 m + 9 = n$

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 9 & -72\\ \hline 15 & -252\\ \hline 16 & -270\\ \hline 19& -324\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 9 & -72\\ \hline 15 & -252\\ \hline 16 & -270\\ \hline 19& -324\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 9 & -71\\ \hline 15 & -124\\ \hline 16 & -132\\ \hline 19& -158\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 9 & -71\\ \hline 15 & -124\\ \hline 16 & -132\\ \hline 19& -158\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 9 & -72\\ \hline 15 & -126\\ \hline 16 & -135\\ \hline 19& -162\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 9 & -72\\ \hline 15 & -126\\ \hline 16 & -135\\ \hline 19& -162\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 9\\ \hline 5 & -36\\ \hline 10 & -70\\ \hline 15& -116\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 9\\ \hline 5 & -36\\ \hline 10 & -70\\ \hline 15& -116\\ \hline \end{tabular}}$

Correct answer:

Explanation:

In the equation $\displaystyle - 9 m + 9 = n$, {m} $\displaystyle {m}$ is the independent variable and {m} $\displaystyle {m}$ is the dependent variable. This means, as we manipulate {m} $\displaystyle {m}$, {n} $\displaystyle {n}$ will change.

Let's start by testing values from the following table:

$\displaystyle {-9(9)+9=-71}$

$\displaystyle {-81+9=-71}$

${-72\neq -71}$ $\displaystyle {-72\neq -71}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} $\displaystyle {m}$ and {n} $\displaystyle {n}$ if $\displaystyle {- 9 m + 9 = n}$ ; thus, this answer choice is not correct and can be eliminated.

Next, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -9\\ \hline 9 & -144\\ \hline 10 & -162\\ \hline 14& -234\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -9\\ \hline 9 & -144\\ \hline 10 & -162\\ \hline 14& -234\\ \hline \end{tabular}}$

$\displaystyle {-9(2)+9=-9}$

$\displaystyle {-18+9=-9}$

{-9=-9} $\displaystyle {-9=-9}$

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {-9(9)+9=-144}$

$\displaystyle {-81+9=-144}$

${-72\neq -144}$ $\displaystyle {-72\neq -144}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} $\displaystyle {m}$ and {n} $\displaystyle {n}$ if $\displaystyle {- 9 m + 9 = n}$ ; thus, this answer choice is not correct and can be eliminated.

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 9\\ \hline 5 & -36\\ \hline 10 & -70\\ \hline 15& -126\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 9\\ \hline 5 & -36\\ \hline 10 & -70\\ \hline 15& -126\\ \hline \end{tabular}}$

$\displaystyle {-9(0)+9=9}$

{0+9=9} $\displaystyle {0+9=9}$

{9=9} $\displaystyle {9=9}$

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {-9(5)+9=-36}$

$\displaystyle {-45+9=-36}$

$\displaystyle {-36=-36}$

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {-9(10)+9=-70}$

$\displaystyle {-90+9=-70}$

${-81\neq -70}$ $\displaystyle {-81\neq -70}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} $\displaystyle {m}$ and {n} $\displaystyle {n}$ if $\displaystyle {- 9 m + 9 = n}$ ; thus, this answer choice is not correct and can be eliminated.

Finally, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -9\\ \hline 5 & -36\\ \hline 10 & -81\\ \hline 19& -162\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -9\\ \hline 5 & -36\\ \hline 10 & -81\\ \hline 19& -162\\ \hline \end{tabular}}$

$\displaystyle {-9(2)+9=-9}$

$\displaystyle {-18+9=-9}$

{-9=-9} $\displaystyle {-9=-9}$

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {-9(5)+9=-36}$

$\displaystyle {-45+9=-36}$

$\displaystyle {-36=-36}$

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {-9(10)+9=-81}$

$\displaystyle {-90+9=-81}$

$\displaystyle {-81=-81}$

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {-9(19)+9=-162}$

$\displaystyle {-171+9=-162}$

$\displaystyle {-162=-162}$

All of these values were correct for our equation; thus, this table is our correct answer.

Report an Error

Example Question #26 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between {m} $\displaystyle {m}$ and {n} $\displaystyle {n}$ if $\displaystyle - 2 m + 11 = n$

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 5\\ \hline 5 & 1\\ \hline 12 & -2\\ \hline 15& -9\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 5\\ \hline 5 & 1\\ \hline 12 & -2\\ \hline 15& -9\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & 1\\ \hline 13 & -30\\ \hline 16 & -42\\ \hline 18& -50\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & 1\\ \hline 13 & -30\\ \hline 16 & -42\\ \hline 18& -50\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & 2\\ \hline 13 & -13\\ \hline 16 & -18\\ \hline 18& -21\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & 2\\ \hline 13 & -13\\ \hline 16 & -18\\ \hline 18& -21\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & 1\\ \hline 13 & -15\\ \hline 16 & -21\\ \hline 18& -25\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & 1\\ \hline 13 & -15\\ \hline 16 & -21\\ \hline 18& -25\\ \hline \end{tabular}}$

Correct answer:

Explanation:

In the equation $\displaystyle - 2 m + 11 = n$, {m} $\displaystyle {m}$ is the independent variable and {m} $\displaystyle {m}$ is the dependent variable. This means, as we manipulate {m} $\displaystyle {m}$, {n} $\displaystyle {n}$ will change.

Let's start by testing values from the following table:

$\displaystyle {-2(5)+11=2}$

$\displaystyle {-10+11=2}$

${1\neq 2}$ $\displaystyle {1\neq 2}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} $\displaystyle {m}$ and {n} $\displaystyle {n}$ if $\displaystyle {- 2 m + 11 = n}$ ; thus, this answer choice is not correct and can be eliminated.

Next, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 7\\ \hline 7 & -6\\ \hline 10 & -18\\ \hline 15& -38\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 7\\ \hline 7 & -6\\ \hline 10 & -18\\ \hline 15& -38\\ \hline \end{tabular}}$

$\displaystyle {-2(2)+11=7}$

$\displaystyle {-4+11=7}$

{7=7} $\displaystyle {7=7}$

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {-2(7)+11=-6}$

$\displaystyle {-14+11=-6}$

${-3\neq -6}$ $\displaystyle {-3\neq -6}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} $\displaystyle {m}$ and {n} $\displaystyle {n}$ if $\displaystyle {- 2 m + 11 = n}$ ; thus, this answer choice is not correct and can be eliminated.

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 5\\ \hline 5 & 1\\ \hline 12 & -2\\ \hline 15& -19\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 5\\ \hline 5 & 1\\ \hline 12 & -2\\ \hline 15& -19\\ \hline \end{tabular}}$

$\displaystyle {-2(3)+11=5}$

$\displaystyle {-6+11=5}$

{5=5} $\displaystyle {5=5}$

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {-2(5)+11=1}$

$\displaystyle {-10+11=1}$

{1=1} $\displaystyle {1=1}$

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {-2(12)+11=-2}$

$\displaystyle {-24+11=-2}$

${-13\neq -2}$ $\displaystyle {-13\neq -2}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} $\displaystyle {m}$ and {n} $\displaystyle {n}$ if $\displaystyle {- 2 m + 11 = n}$ ; thus, this answer choice is not correct and can be eliminated.

Finally, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 7\\ \hline 9 & -7\\ \hline 15 & -19\\ \hline 17& -23\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 7\\ \hline 9 & -7\\ \hline 15 & -19\\ \hline 17& -23\\ \hline \end{tabular}}$

$\displaystyle {-2(2)+11=7}$

$\displaystyle {-4+11=7}$

{7=7} $\displaystyle {7=7}$

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {-2(9)+11=-7}$

$\displaystyle {-18+11=-7}$

{-7=-7} $\displaystyle {-7=-7}$

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {-2(15)+11=-19}$

$\displaystyle {-30+11=-19}$

$\displaystyle {-19=-19}$

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {-2(17)+11=-23}$

$\displaystyle {-34+11=-23}$

$\displaystyle {-23=-23}$

All of these values were correct for our equation; thus, this table is our correct answer.

Report an Error

Example Question #27 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between {m} $\displaystyle {m}$ and {n} $\displaystyle {n}$ if $\displaystyle 2 m + 12 = n$

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 12\\ \hline 15 & 42\\ \hline 17 & 46\\ \hline 18& 48\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 12\\ \hline 15 & 42\\ \hline 17 & 46\\ \hline 18& 48\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 12\\ \hline 15 & 84\\ \hline 17 & 92\\ \hline 18& 96\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 12\\ \hline 15 & 84\\ \hline 17 & 92\\ \hline 18& 96\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 18\\ \hline 11 & 34\\ \hline 15 & 53\\ \hline 18& 58\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 18\\ \hline 11 & 34\\ \hline 15 & 53\\ \hline 18& 58\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 13\\ \hline 15 & 44\\ \hline 17 & 49\\ \hline 18& 52\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 13\\ \hline 15 & 44\\ \hline 17 & 49\\ \hline 18& 52\\ \hline \end{tabular}}$

Correct answer:

Explanation:

In the equation $\displaystyle 2 m + 12 = n$, {m} $\displaystyle {m}$ is the independent variable and {m} $\displaystyle {m}$ is the dependent variable. This means, as we manipulate {m} $\displaystyle {m}$, {n} $\displaystyle {n}$ will change.

Let's start by testing values from the following table:

$\displaystyle {2(0)+12=13}$

$\displaystyle {0+12=13}$

${12\neq 13}$ $\displaystyle {12\neq 13}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} $\displaystyle {m}$ and {n} $\displaystyle {n}$ if $\displaystyle {2 m + 12 = n}$ ; thus, this answer choice is not correct and can be eliminated.

Next, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 8 & 28\\ \hline 14 & 80\\ \hline 16 & 88\\ \hline 19& 100\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 8 & 28\\ \hline 14 & 80\\ \hline 16 & 88\\ \hline 19& 100\\ \hline \end{tabular}}$

$\displaystyle {2(8)+12=28}$

$\displaystyle {16+12=28}$

{28=28} $\displaystyle {28=28}$

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {2(14)+12=80}$

$\displaystyle {28+12=80}$

${40\neq 80}$ $\displaystyle {40\neq 80}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} $\displaystyle {m}$ and {n} $\displaystyle {n}$ if $\displaystyle {2 m + 12 = n}$ ; thus, this answer choice is not correct and can be eliminated.

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 18\\ \hline 11 & 34\\ \hline 15 & 53\\ \hline 18& 48\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 18\\ \hline 11 & 34\\ \hline 15 & 53\\ \hline 18& 48\\ \hline \end{tabular}}$

$\displaystyle {2(3)+12=18}$

$\displaystyle {6+12=18}$

{18=18} $\displaystyle {18=18}$

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {2(11)+12=34}$

$\displaystyle {22+12=34}$

{34=34} $\displaystyle {34=34}$

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {2(15)+12=53}$

$\displaystyle {30+12=53}$

${42\neq 53}$ $\displaystyle {42\neq 53}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} $\displaystyle {m}$ and {n} $\displaystyle {n}$ if $\displaystyle {2 m + 12 = n}$ ; thus, this answer choice is not correct and can be eliminated.

Finally, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 18\\ \hline 4 & 20\\ \hline 9 & 30\\ \hline 14& 40\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 18\\ \hline 4 & 20\\ \hline 9 & 30\\ \hline 14& 40\\ \hline \end{tabular}}$

$\displaystyle {2(3)+12=18}$

$\displaystyle {6+12=18}$

{18=18} $\displaystyle {18=18}$

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {2(4)+12=20}$

$\displaystyle {8+12=20}$

{20=20} $\displaystyle {20=20}$

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {2(9)+12=30}$

$\displaystyle {18+12=30}$

{30=30} $\displaystyle {30=30}$

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {2(14)+12=40}$

$\displaystyle {28+12=40}$

{40=40} $\displaystyle {40=40}$

All of these values were correct for our equation; thus, this table is our correct answer.

Report an Error

Example Question #28 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between {m} $\displaystyle {m}$ and {n} $\displaystyle {n}$ if $\displaystyle - 5 m + 19 = n$

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 19\\ \hline 1 & 14\\ \hline 6 & -11\\ \hline 13& -46\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 19\\ \hline 1 & 14\\ \hline 6 & -11\\ \hline 13& -46\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 19\\ \hline 1 & 28\\ \hline 6 & -22\\ \hline 13& -92\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 19\\ \hline 1 & 28\\ \hline 6 & -22\\ \hline 13& -92\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 19\\ \hline 5 & -6\\ \hline 12 & -30\\ \hline 16& -51\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 19\\ \hline 5 & -6\\ \hline 12 & -30\\ \hline 16& -51\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 20\\ \hline 1 & 16\\ \hline 6 & -8\\ \hline 13& -42\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 20\\ \hline 1 & 16\\ \hline 6 & -8\\ \hline 13& -42\\ \hline \end{tabular}}$

Correct answer:

Explanation:

In the equation $\displaystyle - 5 m + 19 = n$, {m} $\displaystyle {m}$ is the independent variable and {m} $\displaystyle {m}$ is the dependent variable. This means, as we manipulate {m} $\displaystyle {m}$, {n} $\displaystyle {n}$ will change.

Let's start by testing values from the following table:

$\displaystyle {-5(0)+19=20}$

$\displaystyle {0+19=20}$

${19\neq 20}$ $\displaystyle {19\neq 20}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} $\displaystyle {m}$ and {n} $\displaystyle {n}$ if $\displaystyle {- 5 m + 19 = n}$ ; thus, this answer choice is not correct and can be eliminated.

Next, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & -6\\ \hline 8 & -42\\ \hline 9 & -52\\ \hline 17& -132\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & -6\\ \hline 8 & -42\\ \hline 9 & -52\\ \hline 17& -132\\ \hline \end{tabular}}$

$\displaystyle {-5(5)+19=-6}$

$\displaystyle {-25+19=-6}$

{-6=-6} $\displaystyle {-6=-6}$

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {-5(8)+19=-42}$

$\displaystyle {-40+19=-42}$

${-21\neq -42}$ $\displaystyle {-21\neq -42}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} $\displaystyle {m}$ and {n} $\displaystyle {n}$ if $\displaystyle {- 5 m + 19 = n}$ ; thus, this answer choice is not correct and can be eliminated.

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 19\\ \hline 5 & -6\\ \hline 12 & -30\\ \hline 16& -61\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 19\\ \hline 5 & -6\\ \hline 12 & -30\\ \hline 16& -61\\ \hline \end{tabular}}$

$\displaystyle {-5(0)+19=19}$

$\displaystyle {0+19=19}$

{19=19} $\displaystyle {19=19}$

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {-5(5)+19=-6}$

$\displaystyle {-25+19=-6}$

{-6=-6} $\displaystyle {-6=-6}$

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {-5(12)+19=-30}$

$\displaystyle {-60+19=-30}$

${-41\neq -30}$ $\displaystyle {-41\neq -30}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} $\displaystyle {m}$ and {n} $\displaystyle {n}$ if $\displaystyle {- 5 m + 19 = n}$ ; thus, this answer choice is not correct and can be eliminated.

Finally, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 11 & -36\\ \hline 13 & -46\\ \hline 14 & -51\\ \hline 15& -56\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 11 & -36\\ \hline 13 & -46\\ \hline 14 & -51\\ \hline 15& -56\\ \hline \end{tabular}}$

$\displaystyle {-5(11)+19=-36}$

$\displaystyle {-55+19=-36}$

$\displaystyle {-36=-36}$

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {-5(13)+19=-46}$

$\displaystyle {-65+19=-46}$

$\displaystyle {-46=-46}$

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {-5(14)+19=-51}$

$\displaystyle {-70+19=-51}$

$\displaystyle {-51=-51}$

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {-5(15)+19=-56}$

$\displaystyle {-75+19=-56}$

$\displaystyle {-56=-56}$

All of these values were correct for our equation; thus, this table is our correct answer.

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Example Question #29 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between {m} $\displaystyle {m}$ and {n} $\displaystyle {n}$ if $\displaystyle - 12 m + 6 = n$

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 6\\ \hline 1 & -6\\ \hline 7 & -78\\ \hline 15& -174\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 6\\ \hline 1 & -6\\ \hline 7 & -78\\ \hline 15& -174\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 7\\ \hline 1 & -4\\ \hline 7 & -75\\ \hline 15& -170\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 7\\ \hline 1 & -4\\ \hline 7 & -75\\ \hline 15& -170\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & -30\\ \hline 6 & -66\\ \hline 7 & -67\\ \hline 9& -92\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & -30\\ \hline 6 & -66\\ \hline 7 & -67\\ \hline 9& -92\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 6\\ \hline 1 & -12\\ \hline 7 & -156\\ \hline 15& -348\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 6\\ \hline 1 & -12\\ \hline 7 & -156\\ \hline 15& -348\\ \hline \end{tabular}}$

Correct answer:

Explanation:

In the equation $\displaystyle - 12 m + 6 = n$, {m} $\displaystyle {m}$ is the independent variable and {m} $\displaystyle {m}$ is the dependent variable. This means, as we manipulate {m} $\displaystyle {m}$, {n} $\displaystyle {n}$ will change.

Let's start by testing values from the following table:

$\displaystyle {-12(0)+6=7}$

{0+6=7} $\displaystyle {0+6=7}$

${6\neq 7}$ $\displaystyle {6\neq 7}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} $\displaystyle {m}$ and {n} $\displaystyle {n}$ if $\displaystyle {- 12 m + 6 = n}$ ; thus, this answer choice is not correct and can be eliminated.

Next, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 6 & -66\\ \hline 8 & -180\\ \hline 14 & -324\\ \hline 19& -444\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 6 & -66\\ \hline 8 & -180\\ \hline 14 & -324\\ \hline 19& -444\\ \hline \end{tabular}}$

$\displaystyle {-12(6)+6=-66}$

$\displaystyle {-72+6=-66}$

$\displaystyle {-66=-66}$

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {-12(8)+6=-180}$

$\displaystyle {-96+6=-180}$

${-90\neq -180}$ $\displaystyle {-90\neq -180}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} $\displaystyle {m}$ and {n} $\displaystyle {n}$ if $\displaystyle {- 12 m + 6 = n}$ ; thus, this answer choice is not correct and can be eliminated.

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & -30\\ \hline 6 & -66\\ \hline 7 & -67\\ \hline 9& -102\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & -30\\ \hline 6 & -66\\ \hline 7 & -67\\ \hline 9& -102\\ \hline \end{tabular}}$

$\displaystyle {-12(3)+6=-30}$

$\displaystyle {-36+6=-30}$

$\displaystyle {-30=-30}$

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {-12(6)+6=-66}$

$\displaystyle {-72+6=-66}$

$\displaystyle {-66=-66}$

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {-12(7)+6=-67}$

$\displaystyle {-84+6=-67}$

${-78\neq -67}$ $\displaystyle {-78\neq -67}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} $\displaystyle {m}$ and {n} $\displaystyle {n}$ if $\displaystyle {- 12 m + 6 = n}$ ; thus, this answer choice is not correct and can be eliminated.

Finally, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -18\\ \hline 7 & -78\\ \hline 14 & -162\\ \hline 18& -210\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -18\\ \hline 7 & -78\\ \hline 14 & -162\\ \hline 18& -210\\ \hline \end{tabular}}$

$\displaystyle {-12(2)+6=-18}$

$\displaystyle {-24+6=-18}$

$\displaystyle {-18=-18}$

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {-12(7)+6=-78}$

$\displaystyle {-84+6=-78}$

$\displaystyle {-78=-78}$

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {-12(14)+6=-162}$

$\displaystyle {-168+6=-162}$

$\displaystyle {-162=-162}$

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {-12(18)+6=-210}$

$\displaystyle {-216+6=-210}$

$\displaystyle {-210=-210}$

All of these values were correct for our equation; thus, this table is our correct answer.

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Example Question #30 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between {m} $\displaystyle {m}$ and {n} $\displaystyle {n}$ if $\displaystyle m - 1 = n$

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 3\\ \hline 10 & 11\\ \hline 11 & 13\\ \hline 17& 20\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 3\\ \hline 10 & 11\\ \hline 11 & 13\\ \hline 17& 20\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -1\\ \hline 6 & 5\\ \hline 8 & 18\\ \hline 14& 23\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -1\\ \hline 6 & 5\\ \hline 8 & 18\\ \hline 14& 23\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 2\\ \hline 10 & 18\\ \hline 11 & 20\\ \hline 17& 32\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 2\\ \hline 10 & 18\\ \hline 11 & 20\\ \hline 17& 32\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 2\\ \hline 10 & 9\\ \hline 11 & 10\\ \hline 17& 16\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 2\\ \hline 10 & 9\\ \hline 11 & 10\\ \hline 17& 16\\ \hline \end{tabular}}$

Correct answer:

Explanation:

In the equation $\displaystyle m - 1 = n$, {m} $\displaystyle {m}$ is the independent variable and {m} $\displaystyle {m}$ is the dependent variable. This means, as we manipulate {m} $\displaystyle {m}$, {n} $\displaystyle {n}$ will change.

Let's start by testing values from the following table:

$\displaystyle {1(3)+-1=3}$

$\displaystyle {3+-1=3}$

${2\neq 3}$ $\displaystyle {2\neq 3}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} $\displaystyle {m}$ and {n} $\displaystyle {n}$ if $\displaystyle {m - 1 = n}$ ; thus, this answer choice is not correct and can be eliminated.

Next, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 7 & 6\\ \hline 13 & 24\\ \hline 15 & 28\\ \hline 19& 36\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 7 & 6\\ \hline 13 & 24\\ \hline 15 & 28\\ \hline 19& 36\\ \hline \end{tabular}}$

$\displaystyle {1(7)-1=6}$

{7-1=6} $\displaystyle {7-1=6}$

{6=6} $\displaystyle {6=6}$

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {1(13)-1=24}$

$\displaystyle {13-1=24}$

${12\neq 24}$ $\displaystyle {12\neq 24}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} $\displaystyle {m}$ and {n} $\displaystyle {n}$ if $\displaystyle {m - 1 = n}$ ; thus, this answer choice is not correct and can be eliminated.

$\displaystyle {1(0)-1=-1}$

$\displaystyle {0-1=-1}$

{-1=-1} $\displaystyle {-1=-1}$

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {1(6)-1=5}$

{6-1=5} $\displaystyle {6-1=5}$

{5=5} $\displaystyle {5=5}$

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {1(8)-1=18}$

$\displaystyle {8-1=18}$

${7\neq 18}$ $\displaystyle {7\neq 18}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} $\displaystyle {m}$ and {n} $\displaystyle {n}$ if $\displaystyle {m - 1 = n}$ ; thus, this answer choice is not correct and can be eliminated.

Finally, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 0\\ \hline 3 & 2\\ \hline 6 & 5\\ \hline 12& 11\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 0\\ \hline 3 & 2\\ \hline 6 & 5\\ \hline 12& 11\\ \hline \end{tabular}}$

$\displaystyle {1(1)-1=0}$

{1-1=0} $\displaystyle {1-1=0}$

{0=0} $\displaystyle {0=0}$

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {1(3)-1=2}$

{3-1=2} $\displaystyle {3-1=2}$

{2=2} $\displaystyle {2=2}$

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {1(6)-1=5}$

{6-1=5} $\displaystyle {6-1=5}$

{5=5} $\displaystyle {5=5}$

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {1(12)-1=11}$

$\displaystyle {12+-1=11}$

{11=11} $\displaystyle {11=11}$

All of these values were correct for our equation; thus, this table is our correct answer.

Report an Error

Example Question #31 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between {m} $\displaystyle {m}$ and {n} $\displaystyle {n}$ if $\displaystyle 15 m + 8 = n$

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 39\\ \hline 13 & 205\\ \hline 14 & 221\\ \hline 16& 252\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 39\\ \hline 13 & 205\\ \hline 14 & 221\\ \hline 16& 252\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 23\\ \hline 3 & 53\\ \hline 6 & 109\\ \hline 19& 303\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 23\\ \hline 3 & 53\\ \hline 6 & 109\\ \hline 19& 303\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 38\\ \hline 13 & 406\\ \hline 14 & 436\\ \hline 16& 496\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 38\\ \hline 13 & 406\\ \hline 14 & 436\\ \hline 16& 496\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 38\\ \hline 13 & 203\\ \hline 14 & 218\\ \hline 16& 248\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 38\\ \hline 13 & 203\\ \hline 14 & 218\\ \hline 16& 248\\ \hline \end{tabular}}$

Correct answer:

Explanation:

In the equation $\displaystyle 15 m + 8 = n$, {m} $\displaystyle {m}$ is the independent variable and {m} $\displaystyle {m}$ is the dependent variable. This means, as we manipulate {m} $\displaystyle {m}$, {n} $\displaystyle {n}$ will change.

Let's start by testing values from the following table:

$\displaystyle {15(2)+8=39}$

$\displaystyle {30+8=39}$

${38\neq 39}$ $\displaystyle {38\neq 39}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} $\displaystyle {m}$ and {n} $\displaystyle {n}$ if $\displaystyle {15 m + 8 = n}$ ; thus, this answer choice is not correct and can be eliminated.

Next, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 38\\ \hline 3 & 106\\ \hline 7 & 226\\ \hline 8& 256\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 38\\ \hline 3 & 106\\ \hline 7 & 226\\ \hline 8& 256\\ \hline \end{tabular}}$

$\displaystyle {15(2)+8=38}$

$\displaystyle {30+8=38}$

{38=38} $\displaystyle {38=38}$

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {15(3)+8=106}$

$\displaystyle {45+8=106}$

${53\neq 106}$ $\displaystyle {53\neq 106}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} $\displaystyle {m}$ and {n} $\displaystyle {n}$ if $\displaystyle {15 m + 8 = n}$ ; thus, this answer choice is not correct and can be eliminated.

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 23\\ \hline 3 & 53\\ \hline 6 & 109\\ \hline 19& 293\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 23\\ \hline 3 & 53\\ \hline 6 & 109\\ \hline 19& 293\\ \hline \end{tabular}}$

$\displaystyle {15(1)+8=23}$

$\displaystyle {15+8=23}$

{23=23} $\displaystyle {23=23}$

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {15(3)+8=53}$

$\displaystyle {45+8=53}$

{53=53} $\displaystyle {53=53}$

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {15(6)+8=109}$

$\displaystyle {90+8=109}$

${98\neq 109}$ $\displaystyle {98\neq 109}$

Because this equation did not work out, this means that not all of the values from the table are representative of the relationship between {m} $\displaystyle {m}$ and {n} $\displaystyle {n}$ if $\displaystyle {15 m + 8 = n}$ ; thus, this answer choice is not correct and can be eliminated.

Finally, let's test values from the following table:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 53\\ \hline 5 & 83\\ \hline 8 & 128\\ \hline 9& 143\\ \hline \end{tabular}}$ $\displaystyle {\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 53\\ \hline 5 & 83\\ \hline 8 & 128\\ \hline 9& 143\\ \hline \end{tabular}}$

$\displaystyle {15(3)+8=53}$

$\displaystyle {45+8=53}$

{53=53} $\displaystyle {53=53}$

These values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {15(5)+8=83}$

$\displaystyle {75+8=83}$

{83=83} $\displaystyle {83=83}$

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {15(8)+8=128}$

$\displaystyle {120+8=128}$

$\displaystyle {128=128}$

Again, these values are correct for our equation, but to be safe we should plug each value into our equation until we find a value that is not correct, or that each value is correct.

$\displaystyle {15(9)+8=143}$

$\displaystyle {135+8=143}$

$\displaystyle {143=143}$

All of these values were correct for our equation; thus, this table is our correct answer.

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Common Core: 6th Grade Math : Grade 6

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Example Question #22 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

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