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Common Core: 6th Grade Math : Understand Independent and Dependent Variables: CCSS.Math.Content.6.EE.C.9

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Example Questions

Example Question #61 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between {m} and {n} if - 11 m + 9 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -12\\ \hline 3 & -22\\ \hline 4 & -32\\ \hline 11& -108\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -13\\ \hline 3 & -24\\ \hline 4 & -35\\ \hline 11& -112\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & -46\\ \hline 12 & -123\\ \hline 13 & -123\\ \hline 15& -146\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -13\\ \hline 3 & -48\\ \hline 4 & -70\\ \hline 11& -224\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -13\\ \hline 3 & -24\\ \hline 4 & -35\\ \hline 11& -112\\ \hline \end{tabular}}$

Explanation:

In the equation - 11 m + 9 = n , {m} is the independent variable and {m} is the dependent variable. This means, as we manipulate {m} , {n} will change.

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

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -12\\ \hline 3 & -22\\ \hline 4 & -32\\ \hline 11& -108\\ \hline \end{tabular}}$

{-11(2)+9=-12}

{-22+9=-12}

${-13\neq -12}$

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} and {n} if {- 11 m + 9 = n} ; thus, this answer choice is not correct and can be eliminated.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 9\\ \hline 5 & -92\\ \hline 6 & -114\\ \hline 10& -202\\ \hline \end{tabular}}$

{-11(0)+9=9}

{0+9=9}

{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.

{-11(5)+9=-92}

{-55+9=-92}

${-46\neq -92}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & -46\\ \hline 12 & -123\\ \hline 13 & -123\\ \hline 15& -156\\ \hline \end{tabular}}$

{-11(5)+9=-46}

{-55+9=-46}

{-46=-46}

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.

{-11(12)+9=-123}

{-132+9=-123}

{-123=-123}

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.

{-11(13)+9=-123}

{-143+9=-123}

${-134\neq -123}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & -24\\ \hline 5 & -46\\ \hline 10 & -101\\ \hline 12& -123\\ \hline \end{tabular}}$

{-11(3)+9=-24}

{-33+9=-24}

{-24=-24}

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.

{-11(5)+9=-46}

{-55+9=-46}

{-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.

{-11(10)+9=-101}

{-110+9=-101}

{-101=-101}

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.

{-11(12)+9=-123}

{-132+9=-123}

{-123=-123}

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

Report an Error

Example Question #62 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

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

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & 7\\ \hline 10 & 1\\ \hline 14 & -3\\ \hline 19& -8\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & 7\\ \hline 10 & 2\\ \hline 14 & -6\\ \hline 19& -16\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 8\\ \hline 7 & 4\\ \hline 10 & 12\\ \hline 15& 6\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & 8\\ \hline 10 & 3\\ \hline 14 & 0\\ \hline 19& -4\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & 7\\ \hline 10 & 1\\ \hline 14 & -3\\ \hline 19& -8\\ \hline \end{tabular}}$

Explanation:

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

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & 8\\ \hline 10 & 3\\ \hline 14 & 0\\ \hline 19& -4\\ \hline \end{tabular}}$

{-1(4)+11=8}

{-4+11=8}

${7\neq 8}$

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} and {n} if {- m + 11 = n} ; thus, this answer choice is not correct and can be eliminated.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & 7\\ \hline 7 & 8\\ \hline 11 & 0\\ \hline 14& -6\\ \hline \end{tabular}}$

{-1(4)+11=7}

{-4+11=7}

{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.

{-1(7)+11=8}

{-7+11=8}

${4\neq 8}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 8\\ \hline 7 & 4\\ \hline 10 & 12\\ \hline 15& -4\\ \hline \end{tabular}}$

{-1(3)+11=8}

{-3+11=8}

{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.

{-1(7)+11=4}

{-7+11=4}

{4=4}

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.

{-1(10)+11=12}

{-10+11=12}

${1\neq 12}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 11\\ \hline 11 & 0\\ \hline 12 & -1\\ \hline 13& -2\\ \hline \end{tabular}}$

{-1(0)+11=11}

{0+11=11}

{11=11}

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.

{-1(11)+11=0}

{-11+11=0}

{0=0}

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.

{-1(12)+11=-1}

{-12+11=-1}

{-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.

{-1(13)+11=-2}

{-13+11=-2}

{-2=-2}

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

Report an Error

Example Question #63 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between {m} and {n} if - 18 m - 8 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -79\\ \hline 12 & -222\\ \hline 14 & -257\\ \hline 16& -292\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -26\\ \hline 7 & -134\\ \hline 11 & -195\\ \hline 16& -286\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -80\\ \hline 12 & -448\\ \hline 14 & -520\\ \hline 16& -592\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -80\\ \hline 12 & -224\\ \hline 14 & -260\\ \hline 16& -296\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -80\\ \hline 12 & -224\\ \hline 14 & -260\\ \hline 16& -296\\ \hline \end{tabular}}$

Explanation:

In the equation - 18 m - 8 = n , {m} is the independent variable and {m} is the dependent variable. This means, as we manipulate {m} , {n} will change.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -79\\ \hline 12 & -222\\ \hline 14 & -257\\ \hline 16& -292\\ \hline \end{tabular}}$

{-18(4)+-8=-79}

{-72+-8=-79}

${-80\neq -79}$

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} and {n} if {- 18 m - 8 = n} ; thus, this answer choice is not correct and can be eliminated.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -44\\ \hline 5 & -196\\ \hline 8 & -304\\ \hline 13& -484\\ \hline \end{tabular}}$

{-18(2)-8=-44}

{-36-8=-44}

{-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.

{-18(5)-8=-196}

{-90-8=-196}

${-98\neq -196}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -26\\ \hline 7 & -134\\ \hline 11 & -195\\ \hline 16& -286\\ \hline \end{tabular}}$

{-18(1)-8=-26}

{-18-8=-26}

{-26=-26}

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.

{-18(7)-8=-134}

{-126-8=-134}

{-134=-134}

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.

{-18(11)-8=-195}

{-198-8=-195}

${-206\neq -195}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -44\\ \hline 3 & -62\\ \hline 6 & -116\\ \hline 12& -224\\ \hline \end{tabular}}$

{-18(2)-8=-44}

{-36-8=-44}

{-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.

{-18(3)-8=-62}

{-54-8=-62}

{-62=-62}

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.

{-18(6)-8=-116}

{-108-8=-116}

{-116=-116}

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.

{-18(12)-8=-224}

{-216+-8=-224}

{-224=-224}

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

Report an Error

Example Question #64 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between {m} and {n} if 19 m + 17 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 74\\ \hline 6 & 131\\ \hline 11 & 237\\ \hline 16& 331\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 56\\ \hline 8 & 171\\ \hline 10 & 210\\ \hline 14& 287\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 55\\ \hline 8 & 338\\ \hline 10 & 414\\ \hline 14& 566\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 55\\ \hline 8 & 169\\ \hline 10 & 207\\ \hline 14& 283\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 55\\ \hline 8 & 169\\ \hline 10 & 207\\ \hline 14& 283\\ \hline \end{tabular}}$

Explanation:

In the equation 19 m + 17 = n , {m} is the independent variable and {m} is the dependent variable. This means, as we manipulate {m} , {n} will change.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 56\\ \hline 8 & 171\\ \hline 10 & 210\\ \hline 14& 287\\ \hline \end{tabular}}$

{19(2)+17=56}

{38+17=56}

${55\neq 56}$

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} and {n} if {19 m + 17 = n} ; thus, this answer choice is not correct and can be eliminated.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & 112\\ \hline 8 & 338\\ \hline 10 & 414\\ \hline 13& 528\\ \hline \end{tabular}}$

{19(5)+17=112}

{95+17=112}

{112=112}

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.

{19(8)+17=338}

{152+17=338}

${169\neq 338}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 74\\ \hline 6 & 131\\ \hline 11 & 237\\ \hline 16& 321\\ \hline \end{tabular}}$

{19(3)+17=74}

{57+17=74}

{74=74}

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.

{19(6)+17=131}

{114+17=131}

{131=131}

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.

{19(11)+17=237}

{209+17=237}

${226\neq 237}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 36\\ \hline 4 & 93\\ \hline 8 & 169\\ \hline 9& 188\\ \hline \end{tabular}}$

{19(1)+17=36}

{19+17=36}

{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.

{19(4)+17=93}

{76+17=93}

{93=93}

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.

{19(8)+17=169}

{152+17=169}

{169=169}

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.

{19(9)+17=188}

{171+17=188}

{188=188}

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

Report an Error

Example Question #65 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

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

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 14 & -39\\ \hline 15 & -41\\ \hline 16 & -32\\ \hline 19& -39\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -13\\ \hline 5 & -21\\ \hline 9 & -29\\ \hline 14& -39\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -12\\ \hline 5 & -19\\ \hline 9 & -26\\ \hline 14& -35\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -13\\ \hline 5 & -42\\ \hline 9 & -58\\ \hline 14& -78\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -13\\ \hline 5 & -21\\ \hline 9 & -29\\ \hline 14& -39\\ \hline \end{tabular}}$

Explanation:

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

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -12\\ \hline 5 & -19\\ \hline 9 & -26\\ \hline 14& -35\\ \hline \end{tabular}}$

{-2(1)+-11=-12}

{-2+-11=-12}

${-13\neq -12}$

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} and {n} if {- 2 m - 11 = n} ; thus, this answer choice is not correct and can be eliminated.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -11\\ \hline 7 & -50\\ \hline 9 & -58\\ \hline 18& -94\\ \hline \end{tabular}}$

{-2(0)-11=-11}

{0-11=-11}

{-11=-11}

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.

{-2(7)-11=-50}

{-14-11=-50}

${-25\neq -50}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 14 & -39\\ \hline 15 & -41\\ \hline 16 & -32\\ \hline 19& -39\\ \hline \end{tabular}}$

{-2(14)-11=-39}

{-28-11=-39}

{-39=-39}

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.

{-2(15)-11=-41}

{-30-11=-41}

{-41=-41}

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.

{-2(16)-11=-32}

{-32-11=-32}

${-43\neq -32}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & -21\\ \hline 7 & -25\\ \hline 9 & -29\\ \hline 11& -33\\ \hline \end{tabular}}$

{-2(5)-11=-21}

{-10-11=-21}

{-21=-21}

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.

{-2(7)-11=-25}

{-14-11=-25}

{-25=-25}

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.

{-2(9)-11=-29}

{-18-11=-29}

{-29=-29}

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.

{-2(11)-11=-33}

{-22+-11=-33}

{-33=-33}

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

Report an Error

Example Question #66 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between {m} and {n} if 4 m = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 0\\ \hline 7 & 56\\ \hline 9 & 72\\ \hline 17& 136\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 0\\ \hline 7 & 28\\ \hline 9 & 36\\ \hline 17& 68\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 1\\ \hline 7 & 30\\ \hline 9 & 39\\ \hline 17& 72\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 0\\ \hline 6 & 24\\ \hline 12 & 59\\ \hline 18& 82\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 0\\ \hline 7 & 28\\ \hline 9 & 36\\ \hline 17& 68\\ \hline \end{tabular}}$

Explanation:

In the equation 4 m = n , {m} is the independent variable and {m} is the dependent variable. This means, as we manipulate {m} , {n} will change.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 1\\ \hline 7 & 30\\ \hline 9 & 39\\ \hline 17& 72\\ \hline \end{tabular}}$

{4(0)+0=1}

{0+0=1}

${0\neq 1}$

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} and {n} if {4 m = n} ; thus, this answer choice is not correct and can be eliminated.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 4\\ \hline 5 & 40\\ \hline 16 & 128\\ \hline 18& 144\\ \hline \end{tabular}}$

{4(1)+0=4}

{4+0=4}

{4=4}

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.

{4(5)+0=40}

{20+0=40}

${20\neq 40}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 0\\ \hline 6 & 24\\ \hline 12 & 59\\ \hline 18& 72\\ \hline \end{tabular}}$

{4(0)+0=0}

{0+0=0}

{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.

{4(6)+0=24}

{24+0=24}

{24=24}

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.

{4(12)+0=59}

{48+0=59}

${48\neq 59}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 11 & 44\\ \hline 13 & 52\\ \hline 14 & 56\\ \hline 19& 76\\ \hline \end{tabular}}$

{4(11)+0=44}

{44+0=44}

{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.

{4(13)+0=52}

{52+0=52}

{52=52}

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.

{4(14)+0=56}

{56+0=56}

{56=56}

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.

{4(19)+0=76}

{76+0=76}

{76=76}

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

Report an Error

Example Question #67 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between {m} and {n} if - 20 m + 4 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 4\\ \hline 1 & -32\\ \hline 11 & -432\\ \hline 18& -712\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 4\\ \hline 1 & -16\\ \hline 11 & -216\\ \hline 18& -356\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -76\\ \hline 10 & -196\\ \hline 11 & -205\\ \hline 14& -266\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 5\\ \hline 1 & -14\\ \hline 11 & -213\\ \hline 18& -352\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 4\\ \hline 1 & -16\\ \hline 11 & -216\\ \hline 18& -356\\ \hline \end{tabular}}$

Explanation:

In the equation - 20 m + 4 = n , {m} is the independent variable and {m} is the dependent variable. This means, as we manipulate {m} , {n} will change.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 5\\ \hline 1 & -14\\ \hline 11 & -213\\ \hline 18& -352\\ \hline \end{tabular}}$

{-20(0)+4=5}

{0+4=5}

${4\neq 5}$

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} and {n} if {- 20 m + 4 = n} ; thus, this answer choice is not correct and can be eliminated.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 8 & -156\\ \hline 9 & -352\\ \hline 18 & -712\\ \hline 19& -752\\ \hline \end{tabular}}$

{-20(8)+4=-156}

{-160+4=-156}

{-156=-156}

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.

{-20(9)+4=-352}

{-180+4=-352}

${-176\neq -352}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -76\\ \hline 10 & -196\\ \hline 11 & -205\\ \hline 14& -276\\ \hline \end{tabular}}$

{-20(4)+4=-76}

{-80+4=-76}

{-76=-76}

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.

{-20(10)+4=-196}

{-200+4=-196}

{-196=-196}

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.

{-20(11)+4=-205}

{-220+4=-205}

${-216\neq -205}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & -96\\ \hline 6 & -116\\ \hline 7 & -136\\ \hline 13& -256\\ \hline \end{tabular}}$

{-20(5)+4=-96}

{-100+4=-96}

{-96=-96}

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.

{-20(6)+4=-116}

{-120+4=-116}

{-116=-116}

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.

{-20(7)+4=-136}

{-140+4=-136}

{-136=-136}

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.

{-20(13)+4=-256}

{-260+4=-256}

{-256=-256}

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

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Example Question #68 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between {m} and {n} if 6 m + 5 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & 29\\ \hline 5 & 35\\ \hline 11 & 82\\ \hline 17& 117\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 5\\ \hline 5 & 35\\ \hline 13 & 83\\ \hline 16& 101\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 5\\ \hline 5 & 70\\ \hline 13 & 166\\ \hline 16& 202\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 6\\ \hline 5 & 37\\ \hline 13 & 86\\ \hline 16& 105\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 5\\ \hline 5 & 35\\ \hline 13 & 83\\ \hline 16& 101\\ \hline \end{tabular}}$

Explanation:

In the equation 6 m + 5 = n , {m} is the independent variable and {m} is the dependent variable. This means, as we manipulate {m} , {n} will change.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 6\\ \hline 5 & 37\\ \hline 13 & 86\\ \hline 16& 105\\ \hline \end{tabular}}$

{6(0)+5=6}

{0+5=6}

${5\neq 6}$

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} and {n} if {6 m + 5 = n} ; thus, this answer choice is not correct and can be eliminated.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 5\\ \hline 2 & 34\\ \hline 8 & 106\\ \hline 11& 142\\ \hline \end{tabular}}$

{6(0)+5=5}

{0+5=5}

{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.

{6(2)+5=34}

{12+5=34}

${17\neq 34}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & 29\\ \hline 5 & 35\\ \hline 11 & 82\\ \hline 17& 107\\ \hline \end{tabular}}$

{6(4)+5=29}

{24+5=29}

{29=29}

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.

{6(5)+5=35}

{30+5=35}

{35=35}

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.

{6(11)+5=82}

{66+5=82}

${71\neq 82}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 5\\ \hline 2 & 17\\ \hline 9 & 59\\ \hline 15& 95\\ \hline \end{tabular}}$

{6(0)+5=5}

{0+5=5}

{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.

{6(2)+5=17}

{12+5=17}

{17=17}

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.

{6(9)+5=59}

{54+5=59}

{59=59}

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.

{6(15)+5=95}

{90+5=95}

{95=95}

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

Report an Error

Example Question #69 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between {m} and {n} if 7 m + 19 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 20\\ \hline 11 & 98\\ \hline 12 & 106\\ \hline 17& 142\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 19\\ \hline 11 & 96\\ \hline 12 & 114\\ \hline 18& 155\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 19\\ \hline 11 & 192\\ \hline 12 & 206\\ \hline 17& 276\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 19\\ \hline 11 & 96\\ \hline 12 & 103\\ \hline 17& 138\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 19\\ \hline 11 & 96\\ \hline 12 & 103\\ \hline 17& 138\\ \hline \end{tabular}}$

Explanation:

In the equation 7 m + 19 = n , {m} is the independent variable and {m} is the dependent variable. This means, as we manipulate {m} , {n} will change.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 20\\ \hline 11 & 98\\ \hline 12 & 106\\ \hline 17& 142\\ \hline \end{tabular}}$

{7(0)+19=20}

{0+19=20}

${19\neq 20}$

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} and {n} if {7 m + 19 = n} ; thus, this answer choice is not correct and can be eliminated.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 19\\ \hline 1 & 52\\ \hline 6 & 122\\ \hline 16& 262\\ \hline \end{tabular}}$

{7(0)+19=19}

{0+19=19}

{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.

{7(1)+19=52}

{7+19=52}

${26\neq 52}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 19\\ \hline 11 & 96\\ \hline 12 & 114\\ \hline 18& 145\\ \hline \end{tabular}}$

{7(0)+19=19}

{0+19=19}

{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.

{7(11)+19=96}

{77+19=96}

{96=96}

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.

{7(12)+19=114}

{84+19=114}

${103\neq 114}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 40\\ \hline 5 & 54\\ \hline 11 & 96\\ \hline 19& 152\\ \hline \end{tabular}}$

{7(3)+19=40}

{21+19=40}

{40=40}

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.

{7(5)+19=54}

{35+19=54}

{54=54}

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.

{7(11)+19=96}

{77+19=96}

{96=96}

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.

{7(19)+19=152}

{133+19=152}

{152=152}

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

Report an Error

Example Question #70 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

Select the table of values that represent the relationship between {m} and {n} if -2 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & -2\\ \hline 5 & -2\\ \hline 12 & 9\\ \hline 16& 8\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & -1\\ \hline 8 & 0\\ \hline 10 & 1\\ \hline 18& 2\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & -2\\ \hline 8 & -4\\ \hline 10 & -4\\ \hline 18& -4\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & -2\\ \hline 8 & -2\\ \hline 10 & -2\\ \hline 18& -2\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & -2\\ \hline 8 & -2\\ \hline 10 & -2\\ \hline 18& -2\\ \hline \end{tabular}}$

Explanation:

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

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & -1\\ \hline 8 & 0\\ \hline 10 & 1\\ \hline 18& 2\\ \hline \end{tabular}}$

{0(5)+-2=-1}

{0+-2=-1}

${-2\neq -1}$

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} and {n} if {-2 = n} ; thus, this answer choice is not correct and can be eliminated.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & -2\\ \hline 6 & -4\\ \hline 11 & -4\\ \hline 18& -4\\ \hline \end{tabular}}$

{0(5)-2=-2}

{0-2=-2}

{-2=-2}

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.

{0(6)-2=-4}

{0-2=-4}

${-2\neq -4}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & -2\\ \hline 5 & -2\\ \hline 12 & 9\\ \hline 16& 8\\ \hline \end{tabular}}$

{0(3)-2=-2}

{0-2=-2}

{-2=-2}

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.

{0(5)-2=-2}

{0-2=-2}

{-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.

{0(12)-2=9}

{0-2=9}

${-2\neq 9}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & -2\\ \hline 7 & -2\\ \hline 8 & -2\\ \hline 9& -2\\ \hline \end{tabular}}$

{0(3)-2=-2}

{0-2=-2}

{-2=-2}

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.

{0(7)-2=-2}

{0-2=-2}

{-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.

{0(8)-2=-2}

{0-2=-2}

{-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.

{0(9)-2=-2}

{0+-2=-2}

{-2=-2}

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 : Understand Independent and Dependent Variables: CCSS.Math.Content.6.EE.C.9

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