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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 #41 : 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 - 5 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -41\\ \hline 6 & -113\\ \hline 9 & -167\\ \hline 10& -185\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -40\\ \hline 6 & -111\\ \hline 9 & -164\\ \hline 10& -181\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 13 & -239\\ \hline 14 & -257\\ \hline 18 & -318\\ \hline 19& -337\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -41\\ \hline 6 & -226\\ \hline 9 & -334\\ \hline 10& -370\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -41\\ \hline 6 & -113\\ \hline 9 & -167\\ \hline 10& -185\\ \hline \end{tabular}}$

Explanation:

In the equation - 18 m - 5 = 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:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -40\\ \hline 6 & -111\\ \hline 9 & -164\\ \hline 10& -181\\ \hline \end{tabular}}$

{-18(2)+-5=-40}

{-36+-5=-40}

${-41\neq -40}$

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

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -5\\ \hline 3 & -118\\ \hline 11 & -406\\ \hline 17& -622\\ \hline \end{tabular}}$

{-18(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.

{-18(3)-5=-118}

{-54-5=-118}

${-59\neq -118}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 13 & -239\\ \hline 14 & -257\\ \hline 18 & -318\\ \hline 19& -337\\ \hline \end{tabular}}$

{-18(13)-5=-239}

{-234-5=-239}

{-239=-239}

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(14)-5=-257}

{-252-5=-257}

{-257=-257}

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(18)-5=-318}

{-324-5=-318}

${-329\neq -318}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -5\\ \hline 3 & -59\\ \hline 8 & -149\\ \hline 14& -257\\ \hline \end{tabular}}$

{-18(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.

{-18(3)-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.

{-18(8)-5=-149}

{-144-5=-149}

{-149=-149}

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(14)-5=-257}

{-252+-5=-257}

{-257=-257}

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

Report an Error

Example Question #42 : 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 9 m - 7 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -7\\ \hline 1 & 4\\ \hline 7 & 112\\ \hline 8& 130\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -6\\ \hline 1 & 4\\ \hline 7 & 59\\ \hline 8& 69\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -7\\ \hline 1 & 2\\ \hline 7 & 56\\ \hline 8& 65\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -7\\ \hline 2 & 11\\ \hline 10 & 94\\ \hline 18& 165\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -7\\ \hline 1 & 2\\ \hline 7 & 56\\ \hline 8& 65\\ \hline \end{tabular}}$

Explanation:

In the equation 9 m - 7 = 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:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -6\\ \hline 1 & 4\\ \hline 7 & 59\\ \hline 8& 69\\ \hline \end{tabular}}$

{9(0)+-7=-6}

{0+-7=-6}

${-7\neq -6}$

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

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -7\\ \hline 9 & 148\\ \hline 11 & 184\\ \hline 13& 220\\ \hline \end{tabular}}$

{9(0)-7=-7}

{0-7=-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.

{9(9)-7=148}

{81-7=148}

${74\neq 148}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -7\\ \hline 2 & 11\\ \hline 10 & 94\\ \hline 18& 165\\ \hline \end{tabular}}$

{9(0)-7=-7}

{0-7=-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.

{9(2)-7=11}

{18-7=11}

{11=11}

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.

{9(10)-7=94}

{90-7=94}

${83\neq 94}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 2\\ \hline 8 & 65\\ \hline 9 & 74\\ \hline 18& 155\\ \hline \end{tabular}}$

{9(1)-7=2}

{9-7=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.

{9(8)-7=65}

{72-7=65}

{65=65}

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.

{9(9)-7=74}

{81-7=74}

{74=74}

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.

{9(18)-7=155}

{162+-7=155}

{155=155}

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

Report an Error

Example Question #43 : 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 13 m + 12 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & 64\\ \hline 9 & 129\\ \hline 11 & 155\\ \hline 17& 233\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & 65\\ \hline 9 & 131\\ \hline 11 & 158\\ \hline 17& 237\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 25\\ \hline 6 & 90\\ \hline 7 & 114\\ \hline 9& 139\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & 64\\ \hline 9 & 258\\ \hline 11 & 310\\ \hline 17& 466\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & 64\\ \hline 9 & 129\\ \hline 11 & 155\\ \hline 17& 233\\ \hline \end{tabular}}$

Explanation:

In the equation 13 m + 12 = 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:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & 65\\ \hline 9 & 131\\ \hline 11 & 158\\ \hline 17& 237\\ \hline \end{tabular}}$

{13(4)+12=65}

{52+12=65}

${64\neq 65}$

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 {13 m + 12 = n} ; thus, this answer choice is not correct and can be eliminated.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 25\\ \hline 10 & 284\\ \hline 11 & 310\\ \hline 15& 414\\ \hline \end{tabular}}$

{13(1)+12=25}

{13+12=25}

{25=25}

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.

{13(10)+12=284}

{130+12=284}

${142\neq 284}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 25\\ \hline 6 & 90\\ \hline 7 & 114\\ \hline 9& 129\\ \hline \end{tabular}}$

{13(1)+12=25}

{13+12=25}

{25=25}

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.

{13(6)+12=90}

{78+12=90}

{90=90}

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.

{13(7)+12=114}

{91+12=114}

${103\neq 114}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & 64\\ \hline 5 & 77\\ \hline 14 & 194\\ \hline 19& 259\\ \hline \end{tabular}}$

{13(4)+12=64}

{52+12=64}

{64=64}

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.

{13(5)+12=77}

{65+12=77}

{77=77}

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.

{13(14)+12=194}

{182+12=194}

{194=194}

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.

{13(19)+12=259}

{247+12=259}

{259=259}

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

Report an Error

Example Question #631 : Expressions & Equations

Select the table of values that represent the relationship between {m} and {n} if 14 m - 17 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -2\\ \hline 2 & 13\\ \hline 11 & 140\\ \hline 13& 169\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 7 & 81\\ \hline 8 & 95\\ \hline 13 & 176\\ \hline 16& 217\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -3\\ \hline 2 & 22\\ \hline 11 & 274\\ \hline 13& 330\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -3\\ \hline 2 & 11\\ \hline 11 & 137\\ \hline 13& 165\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -3\\ \hline 2 & 11\\ \hline 11 & 137\\ \hline 13& 165\\ \hline \end{tabular}}$

Explanation:

In the equation 14 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:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -2\\ \hline 2 & 13\\ \hline 11 & 140\\ \hline 13& 169\\ \hline \end{tabular}}$

{14(1)+-17=-2}

{14+-17=-2}

${-3\neq -2}$

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} and {n} if {14 m - 17 = n} ; thus, this answer choice is not correct and can be eliminated.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 10 & 123\\ \hline 11 & 274\\ \hline 16 & 414\\ \hline 18& 470\\ \hline \end{tabular}}$

{14(10)-17=123}

{140-17=123}

{123=123}

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.

{14(11)-17=274}

{154-17=274}

${137\neq 274}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 7 & 81\\ \hline 8 & 95\\ \hline 13 & 176\\ \hline 16& 217\\ \hline \end{tabular}}$

{14(7)-17=81}

{98-17=81}

{81=81}

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.

{14(8)-17=95}

{112-17=95}

{95=95}

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.

{14(13)-17=176}

{182-17=176}

${165\neq 176}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 25\\ \hline 10 & 123\\ \hline 11 & 137\\ \hline 12& 151\\ \hline \end{tabular}}$

{14(3)-17=25}

{42-17=25}

{25=25}

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.

{14(10)-17=123}

{140-17=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.

{14(11)-17=137}

{154-17=137}

{137=137}

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.

{14(12)-17=151}

{168+-17=151}

{151=151}

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

Report an Error

Example Question #641 : Expressions & Equations

Select the table of values that represent the relationship between {m} and {n} if 3 m - 3 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 7 & 18\\ \hline 12 & 66\\ \hline 14 & 78\\ \hline 19& 108\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -3\\ \hline 4 & 9\\ \hline 5 & 23\\ \hline 11& 40\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 7 & 18\\ \hline 12 & 33\\ \hline 14 & 39\\ \hline 19& 54\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 7 & 19\\ \hline 12 & 35\\ \hline 14 & 42\\ \hline 19& 58\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 7 & 18\\ \hline 12 & 33\\ \hline 14 & 39\\ \hline 19& 54\\ \hline \end{tabular}}$

Explanation:

In the equation 3 m - 3 = 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:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 7 & 19\\ \hline 12 & 35\\ \hline 14 & 42\\ \hline 19& 58\\ \hline \end{tabular}}$

{3(7)+-3=19}

{21+-3=19}

${18\neq 19}$

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 {3 m - 3 = n} ; thus, this answer choice is not correct and can be eliminated.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -3\\ \hline 6 & 30\\ \hline 8 & 42\\ \hline 18& 102\\ \hline \end{tabular}}$

{3(0)-3=-3}

{0-3=-3}

{-3=-3}

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.

{3(6)-3=30}

{18-3=30}

${15\neq 30}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -3\\ \hline 4 & 9\\ \hline 5 & 23\\ \hline 11& 40\\ \hline \end{tabular}}$

{3(0)-3=-3}

{0-3=-3}

{-3=-3}

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.

{3(4)-3=9}

{12-3=9}

{9=9}

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.

{3(5)-3=23}

{15-3=23}

${12\neq 23}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 3\\ \hline 4 & 9\\ \hline 6 & 15\\ \hline 17& 48\\ \hline \end{tabular}}$

{3(2)-3=3}

{6-3=3}

{3=3}

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.

{3(4)-3=9}

{12-3=9}

{9=9}

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.

{3(6)-3=15}

{18-3=15}

{15=15}

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.

{3(17)-3=48}

{51+-3=48}

{48=48}

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

Report an Error

Example Question #642 : Expressions & Equations

Select the table of values that represent the relationship between {m} and {n} if 10 m - 11 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 19\\ \hline 5 & 78\\ \hline 6 & 98\\ \hline 10& 178\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 19\\ \hline 5 & 39\\ \hline 6 & 49\\ \hline 10& 89\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 20\\ \hline 5 & 41\\ \hline 6 & 52\\ \hline 10& 93\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 6 & 49\\ \hline 7 & 59\\ \hline 8 & 80\\ \hline 9& 89\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 19\\ \hline 5 & 39\\ \hline 6 & 49\\ \hline 10& 89\\ \hline \end{tabular}}$

Explanation:

In the equation 10 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:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 20\\ \hline 5 & 41\\ \hline 6 & 52\\ \hline 10& 93\\ \hline \end{tabular}}$

{10(3)+-11=20}

{30+-11=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 {10 m - 11 = n} ; thus, this answer choice is not correct and can be eliminated.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & 29\\ \hline 5 & 78\\ \hline 6 & 98\\ \hline 16& 298\\ \hline \end{tabular}}$

{10(4)-11=29}

{40-11=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.

{10(5)-11=78}

{50-11=78}

${39\neq 78}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 6 & 49\\ \hline 7 & 59\\ \hline 8 & 80\\ \hline 9& 89\\ \hline \end{tabular}}$

{10(6)-11=49}

{60-11=49}

{49=49}

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.

{10(7)-11=59}

{70-11=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.

{10(8)-11=80}

{80-11=80}

${69\neq 80}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & 39\\ \hline 8 & 69\\ \hline 10 & 89\\ \hline 19& 179\\ \hline \end{tabular}}$

{10(5)-11=39}

{50-11=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.

{10(8)-11=69}

{80-11=69}

{69=69}

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.

{10(10)-11=89}

{100-11=89}

{89=89}

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.

{10(19)-11=179}

{190+-11=179}

{179=179}

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

Report an Error

Example Question #641 : Expressions & Equations

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

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 5\\ \hline 5 & 200\\ \hline 13 & 504\\ \hline 14& 542\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 5\\ \hline 5 & 100\\ \hline 13 & 252\\ \hline 14& 271\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 6\\ \hline 5 & 102\\ \hline 13 & 255\\ \hline 14& 275\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & 100\\ \hline 14 & 271\\ \hline 16 & 320\\ \hline 19& 376\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 5\\ \hline 5 & 100\\ \hline 13 & 252\\ \hline 14& 271\\ \hline \end{tabular}}$

Explanation:

In the equation 19 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:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 6\\ \hline 5 & 102\\ \hline 13 & 255\\ \hline 14& 275\\ \hline \end{tabular}}$

{19(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 {19 m + 5 = n} ; thus, this answer choice is not correct and can be eliminated.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 7 & 138\\ \hline 11 & 428\\ \hline 18 & 694\\ \hline 19& 732\\ \hline \end{tabular}}$

{19(7)+5=138}

{133+5=138}

{138=138}

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)+5=428}

{209+5=428}

${214\neq 428}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & 100\\ \hline 14 & 271\\ \hline 16 & 320\\ \hline 19& 366\\ \hline \end{tabular}}$

{19(5)+5=100}

{95+5=100}

{100=100}

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(14)+5=271}

{266+5=271}

{271=271}

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(16)+5=320}

{304+5=320}

${309\neq 320}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 24\\ \hline 2 & 43\\ \hline 10 & 195\\ \hline 19& 366\\ \hline \end{tabular}}$

{19(1)+5=24}

{19+5=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.

{19(2)+5=43}

{38+5=43}

{43=43}

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(10)+5=195}

{190+5=195}

{195=195}

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(19)+5=366}

{361+5=366}

{366=366}

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

Report an Error

Example Question #48 : 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 - 10 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & -13\\ \hline 5 & -15\\ \hline 10 & -20\\ \hline 14& -24\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & -13\\ \hline 5 & -30\\ \hline 10 & -40\\ \hline 14& -48\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & -12\\ \hline 5 & -13\\ \hline 10 & -17\\ \hline 14& -20\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 7 & -17\\ \hline 8 & -18\\ \hline 12 & -11\\ \hline 17& -17\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & -13\\ \hline 5 & -15\\ \hline 10 & -20\\ \hline 14& -24\\ \hline \end{tabular}}$

Explanation:

In the equation - m - 10 = 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:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & -12\\ \hline 5 & -13\\ \hline 10 & -17\\ \hline 14& -20\\ \hline \end{tabular}}$

{-1(3)+-10=-12}

{-3+-10=-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 {- m - 10 = n} ; thus, this answer choice is not correct and can be eliminated.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 6 & -16\\ \hline 8 & -36\\ \hline 11 & -42\\ \hline 14& -48\\ \hline \end{tabular}}$

{-1(6)-10=-16}

{-6-10=-16}

{-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.

{-1(8)-10=-36}

{-8-10=-36}

${-18\neq -36}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 7 & -17\\ \hline 8 & -18\\ \hline 12 & -11\\ \hline 17& -17\\ \hline \end{tabular}}$

{-1(7)-10=-17}

{-7-10=-17}

{-17=-17}

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(8)-10=-18}

{-8-10=-18}

{-18=-18}

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)-10=-11}

{-12-10=-11}

${-22\neq -11}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -10\\ \hline 8 & -18\\ \hline 9 & -19\\ \hline 14& -24\\ \hline \end{tabular}}$

{-1(0)-10=-10}

{0-10=-10}

{-10=-10}

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(8)-10=-18}

{-8-10=-18}

{-18=-18}

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(9)-10=-19}

{-9-10=-19}

{-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.

{-1(14)-10=-24}

{-14+-10=-24}

{-24=-24}

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

Report an Error

Example Question #49 : 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 16 m + 14 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 46\\ \hline 6 & 110\\ \hline 12 & 206\\ \hline 19& 318\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 46\\ \hline 6 & 220\\ \hline 12 & 412\\ \hline 19& 636\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 47\\ \hline 6 & 112\\ \hline 12 & 209\\ \hline 19& 322\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 46\\ \hline 9 & 158\\ \hline 14 & 249\\ \hline 17& 296\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 46\\ \hline 6 & 110\\ \hline 12 & 206\\ \hline 19& 318\\ \hline \end{tabular}}$

Explanation:

In the equation 16 m + 14 = 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:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 47\\ \hline 6 & 112\\ \hline 12 & 209\\ \hline 19& 322\\ \hline \end{tabular}}$

{16(2)+14=47}

{32+14=47}

${46\neq 47}$

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 {16 m + 14 = n} ; thus, this answer choice is not correct and can be eliminated.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 62\\ \hline 8 & 284\\ \hline 13 & 444\\ \hline 18& 604\\ \hline \end{tabular}}$

{16(3)+14=62}

{48+14=62}

{62=62}

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.

{16(8)+14=284}

{128+14=284}

${142\neq 284}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 46\\ \hline 9 & 158\\ \hline 14 & 249\\ \hline 17& 286\\ \hline \end{tabular}}$

{16(2)+14=46}

{32+14=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.

{16(9)+14=158}

{144+14=158}

{158=158}

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.

{16(14)+14=249}

{224+14=249}

${238\neq 249}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 46\\ \hline 4 & 78\\ \hline 6 & 110\\ \hline 15& 254\\ \hline \end{tabular}}$

{16(2)+14=46}

{32+14=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.

{16(4)+14=78}

{64+14=78}

{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.

{16(6)+14=110}

{96+14=110}

{110=110}

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.

{16(15)+14=254}

{240+14=254}

{254=254}

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

Report an Error

Example Question #50 : 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:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 6\\ \hline 6 & 1\\ \hline 11 & -8\\ \hline 14& -13\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 5\\ \hline 6 & -1\\ \hline 11 & -11\\ \hline 14& -17\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 5\\ \hline 6 & -2\\ \hline 11 & -22\\ \hline 14& -34\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 9\\ \hline 6 & -1\\ \hline 9 & 4\\ \hline 10& 1\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 5\\ \hline 6 & -1\\ \hline 11 & -11\\ \hline 14& -17\\ \hline \end{tabular}}$

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:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & 6\\ \hline 6 & 1\\ \hline 11 & -8\\ \hline 14& -13\\ \hline \end{tabular}}$

{-2(3)+11=6}

{-6+11=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 {- 2 m + 11 = n} ; thus, this answer choice is not correct and can be eliminated.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 6 & -1\\ \hline 10 & -18\\ \hline 15 & -38\\ \hline 18& -50\\ \hline \end{tabular}}$

{-2(6)+11=-1}

{-12+11=-1}

{-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.

{-2(10)+11=-18}

{-20+11=-18}

${-9\neq -18}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 9\\ \hline 6 & -1\\ \hline 9 & 4\\ \hline 10& -9\\ \hline \end{tabular}}$

{-2(1)+11=9}

{-2+11=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.

{-2(6)+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.

{-2(9)+11=4}

{-18+11=4}

${-7\neq 4}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 9\\ \hline 11 & -11\\ \hline 15 & -19\\ \hline 16& -21\\ \hline \end{tabular}}$

{-2(1)+11=9}

{-2+11=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.

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

{-22+11=-11}

{-11=-11}

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(15)+11=-19}

{-30+11=-19}

{-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.

{-2(16)+11=-21}

{-32+11=-21}

{-21=-21}

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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Example Question #41 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

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Example Question #48 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

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Example Question #50 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9

All Common Core: 6th Grade Math Resources

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