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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

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Example Question #1 : 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 + 3 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & 31\\ \hline 14 & 101\\ \hline 15 & 119\\ \hline 19& 146\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 3\\ \hline 8 & 118\\ \hline 14 & 202\\ \hline 18& 258\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 4\\ \hline 8 & 61\\ \hline 14 & 104\\ \hline 18& 133\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 3\\ \hline 8 & 59\\ \hline 14 & 101\\ \hline 18& 129\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 3\\ \hline 8 & 59\\ \hline 14 & 101\\ \hline 18& 129\\ \hline \end{tabular}}$

Explanation:

In the equation 7 m + 3 = 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:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 4\\ \hline 8 & 61\\ \hline 14 & 104\\ \hline 18& 133\\ \hline \end{tabular}}$

{7(0)+3=4}

{0+3=4}

${3\neq 4}$

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

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 17\\ \hline 7 & 104\\ \hline 8 & 118\\ \hline 10& 146\\ \hline \end{tabular}}$

{7(2)+3=17}

{14+3=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.

{7(7)+3=104}

{49+3=104}

${52\neq 104}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & 31\\ \hline 14 & 101\\ \hline 15 & 119\\ \hline 19& 136\\ \hline \end{tabular}}$

{7(4)+3=31}

{28+3=31}

{31=31}

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(14)+3=101}

{98+3=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.

{7(15)+3=119}

{105+3=119}

${108\neq 119}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 11 & 80\\ \hline 12 & 87\\ \hline 16 & 115\\ \hline 17& 122\\ \hline \end{tabular}}$

{7(11)+3=80}

{77+3=80}

{80=80}

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)+3=87}

{84+3=87}

{87=87}

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(16)+3=115}

{112+3=115}

{115=115}

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(17)+3=122}

{119+3=122}

{122=122}

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

Report an Error

Example Question #2 : 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 + 5 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 5\\ \hline 1 & -16\\ \hline 4 & -94\\ \hline 19& -484\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 6 & -73\\ \hline 10 & -125\\ \hline 17 & -205\\ \hline 18& -219\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 6\\ \hline 1 & -6\\ \hline 4 & -44\\ \hline 19& -238\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 5\\ \hline 1 & -8\\ \hline 4 & -47\\ \hline 19& -242\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 5\\ \hline 1 & -8\\ \hline 4 & -47\\ \hline 19& -242\\ \hline \end{tabular}}$

Explanation:

In the equation - 13 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:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 6\\ \hline 1 & -6\\ \hline 4 & -44\\ \hline 19& -238\\ \hline \end{tabular}}$

{-13(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 {- 13 m + 5 = n} ; thus, this answer choice is not correct and can be eliminated.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -47\\ \hline 9 & -224\\ \hline 13 & -328\\ \hline 17& -432\\ \hline \end{tabular}}$

{-13(4)+5=-47}

{-52+5=-47}

{-47=-47}

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(9)+5=-224}

{-117+5=-224}

${-112\neq -224}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 6 & -73\\ \hline 10 & -125\\ \hline 17 & -205\\ \hline 18& -229\\ \hline \end{tabular}}$

{-13(6)+5=-73}

{-78+5=-73}

{-73=-73}

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)+5=-125}

{-130+5=-125}

{-125=-125}

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(17)+5=-205}

{-221+5=-205}

${-216\neq -205}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 5\\ \hline 4 & -47\\ \hline 15 & -190\\ \hline 17& -216\\ \hline \end{tabular}}$

{-13(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.

{-13(4)+5=-47}

{-52+5=-47}

{-47=-47}

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(15)+5=-190}

{-195+5=-190}

{-190=-190}

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(17)+5=-216}

{-221+5=-216}

{-216=-216}

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

Report an Error

Example Question #3 : 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 - 17 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -6\\ \hline 4 & 27\\ \hline 10 & 104\\ \hline 13& 136\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & 27\\ \hline 5 & 38\\ \hline 12 & 115\\ \hline 16& 159\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & 27\\ \hline 5 & 76\\ \hline 12 & 230\\ \hline 16& 318\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & 28\\ \hline 5 & 40\\ \hline 12 & 118\\ \hline 16& 163\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & 27\\ \hline 5 & 38\\ \hline 12 & 115\\ \hline 16& 159\\ \hline \end{tabular}}$

Explanation:

In the equation 11 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:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & 28\\ \hline 5 & 40\\ \hline 12 & 118\\ \hline 16& 163\\ \hline \end{tabular}}$

{11(4)+-17=28}

{44+-17=28}

${27\neq 28}$

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

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 6 & 49\\ \hline 7 & 120\\ \hline 10 & 186\\ \hline 14& 274\\ \hline \end{tabular}}$

{11(6)-17=49}

{66-17=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.

{11(7)-17=120}

{77-17=120}

${60\neq 120}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -6\\ \hline 4 & 27\\ \hline 10 & 104\\ \hline 13& 136\\ \hline \end{tabular}}$

{11(1)-17=-6}

{11-17=-6}

{-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.

{11(4)-17=27}

{44-17=27}

{27=27}

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)-17=104}

{110-17=104}

${93\neq 104}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 6 & 49\\ \hline 10 & 93\\ \hline 16 & 159\\ \hline 17& 170\\ \hline \end{tabular}}$

{11(6)-17=49}

{66-17=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.

{11(10)-17=93}

{110-17=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.

{11(16)-17=159}

{176-17=159}

{159=159}

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(17)-17=170}

{187+-17=170}

{170=170}

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

Report an Error

Example Question #4 : 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 - 10 m - 7 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -7\\ \hline 3 & -37\\ \hline 6 & -67\\ \hline 19& -197\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -6\\ \hline 3 & -35\\ \hline 6 & -64\\ \hline 19& -193\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -7\\ \hline 3 & -74\\ \hline 6 & -134\\ \hline 19& -394\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & -37\\ \hline 4 & -47\\ \hline 15 & -146\\ \hline 16& -157\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -7\\ \hline 3 & -37\\ \hline 6 & -67\\ \hline 19& -197\\ \hline \end{tabular}}$

Explanation:

In the equation - 10 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:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -6\\ \hline 3 & -35\\ \hline 6 & -64\\ \hline 19& -193\\ \hline \end{tabular}}$

{-10(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 {- 10 m - 7 = n} ; thus, this answer choice is not correct and can be eliminated.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -17\\ \hline 11 & -234\\ \hline 14 & -294\\ \hline 16& -334\\ \hline \end{tabular}}$

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

{-10-7=-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.

{-10(11)-7=-234}

{-110-7=-234}

${-117\neq -234}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & -37\\ \hline 4 & -47\\ \hline 15 & -146\\ \hline 16& -157\\ \hline \end{tabular}}$

{-10(3)-7=-37}

{-30-7=-37}

{-37=-37}

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(4)-7=-47}

{-40-7=-47}

{-47=-47}

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(15)-7=-146}

{-150-7=-146}

${-157\neq -146}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -17\\ \hline 8 & -87\\ \hline 17 & -177\\ \hline 18& -187\\ \hline \end{tabular}}$

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

{-10-7=-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.

{-10(8)-7=-87}

{-80-7=-87}

{-87=-87}

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(17)-7=-177}

{-170-7=-177}

{-177=-177}

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(18)-7=-187}

{-180+-7=-187}

{-187=-187}

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

Report an Error

Example Question #5 : 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 + 10 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & -45\\ \hline 6 & -112\\ \hline 14 & -288\\ \hline 19& -398\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & -44\\ \hline 6 & -54\\ \hline 14 & -141\\ \hline 19& -195\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & -45\\ \hline 6 & -56\\ \hline 14 & -144\\ \hline 19& -199\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 8 & -78\\ \hline 12 & -122\\ \hline 15 & -144\\ \hline 17& -167\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & -45\\ \hline 6 & -56\\ \hline 14 & -144\\ \hline 19& -199\\ \hline \end{tabular}}$

Explanation:

In the equation - 11 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:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & -44\\ \hline 6 & -54\\ \hline 14 & -141\\ \hline 19& -195\\ \hline \end{tabular}}$

{-11(5)+10=-44}

{-55+10=-44}

${-45\neq -44}$

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

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 8 & -78\\ \hline 9 & -178\\ \hline 11 & -222\\ \hline 17& -354\\ \hline \end{tabular}}$

{-11(8)+10=-78}

{-88+10=-78}

{-78=-78}

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(9)+10=-178}

{-99+10=-178}

${-89\neq -178}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 8 & -78\\ \hline 12 & -122\\ \hline 15 & -144\\ \hline 17& -177\\ \hline \end{tabular}}$

{-11(8)+10=-78}

{-88+10=-78}

{-78=-78}

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)+10=-122}

{-132+10=-122}

{-122=-122}

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(15)+10=-144}

{-165+10=-144}

${-155\neq -144}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -12\\ \hline 4 & -34\\ \hline 10 & -100\\ \hline 12& -122\\ \hline \end{tabular}}$

{-11(2)+10=-12}

{-22+10=-12}

{-12=-12}

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(4)+10=-34}

{-44+10=-34}

{-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.

{-11(10)+10=-100}

{-110+10=-100}

{-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.

{-11(12)+10=-122}

{-132+10=-122}

{-122=-122}

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

Report an Error

Example Question #6 : 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 - 11 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & -38\\ \hline 15 & -146\\ \hline 16 & -155\\ \hline 18& -173\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & -37\\ \hline 15 & -144\\ \hline 16 & -152\\ \hline 18& -169\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & -38\\ \hline 15 & -292\\ \hline 16 & -310\\ \hline 18& -346\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 9 & -92\\ \hline 11 & -110\\ \hline 15 & -135\\ \hline 19& -172\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & -38\\ \hline 15 & -146\\ \hline 16 & -155\\ \hline 18& -173\\ \hline \end{tabular}}$

Explanation:

In the equation - 9 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:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 3 & -37\\ \hline 15 & -144\\ \hline 16 & -152\\ \hline 18& -169\\ \hline \end{tabular}}$

{-9(3)+-11=-37}

{-27+-11=-37}

${-38\neq -37}$

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

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 6 & -65\\ \hline 14 & -274\\ \hline 15 & -292\\ \hline 18& -346\\ \hline \end{tabular}}$

{-9(6)-11=-65}

{-54-11=-65}

{-65=-65}

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(14)-11=-274}

{-126-11=-274}

${-137\neq -274}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 9 & -92\\ \hline 11 & -110\\ \hline 15 & -135\\ \hline 19& -172\\ \hline \end{tabular}}$

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

{-81-11=-92}

{-92=-92}

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(11)-11=-110}

{-99-11=-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.

{-9(15)-11=-135}

{-135-11=-135}

${-146\neq -135}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 9 & -92\\ \hline 10 & -101\\ \hline 15 & -146\\ \hline 16& -155\\ \hline \end{tabular}}$

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

{-81-11=-92}

{-92=-92}

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)-11=-101}

{-90-11=-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.

{-9(15)-11=-146}

{-135-11=-146}

{-146=-146}

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(16)-11=-155}

{-144+-11=-155}

{-155=-155}

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

Report an Error

Example Question #7 : 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 + 18 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 6\\ \hline 2 & -6\\ \hline 4 & -31\\ \hline 10& -108\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 5\\ \hline 2 & -16\\ \hline 4 & -68\\ \hline 10& -224\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 5\\ \hline 2 & -8\\ \hline 4 & -34\\ \hline 10& -112\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 5\\ \hline 4 & -34\\ \hline 6 & -49\\ \hline 14& -154\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 5\\ \hline 2 & -8\\ \hline 4 & -34\\ \hline 10& -112\\ \hline \end{tabular}}$

Explanation:

In the equation - 13 m + 18 = 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:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 6\\ \hline 2 & -6\\ \hline 4 & -31\\ \hline 10& -108\\ \hline \end{tabular}}$

{-13(1)+18=6}

{-13+18=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 {- 13 m + 18 = n} ; thus, this answer choice is not correct and can be eliminated.

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 18\\ \hline 4 & -68\\ \hline 6 & -120\\ \hline 14& -328\\ \hline \end{tabular}}$

{-13(0)+18=18}

{0+18=18}

{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.

{-13(4)+18=-68}

{-52+18=-68}

${-34\neq -68}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 5\\ \hline 4 & -34\\ \hline 6 & -49\\ \hline 14& -164\\ \hline \end{tabular}}$

{-13(1)+18=5}

{-13+18=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.

{-13(4)+18=-34}

{-52+18=-34}

{-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.

{-13(6)+18=-49}

{-78+18=-49}

${-60\neq -49}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 18\\ \hline 7 & -73\\ \hline 11 & -125\\ \hline 14& -164\\ \hline \end{tabular}}$

{-13(0)+18=18}

{0+18=18}

{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.

{-13(7)+18=-73}

{-91+18=-73}

{-73=-73}

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(11)+18=-125}

{-143+18=-125}

{-125=-125}

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)+18=-164}

{-182+18=-164}

{-164=-164}

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

Report an Error

Example Question #8 : 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 - 19 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -1\\ \hline 2 & 34\\ \hline 11 & 358\\ \hline 13& 430\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & 71\\ \hline 11 & 179\\ \hline 16 & 280\\ \hline 17& 297\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 0\\ \hline 2 & 19\\ \hline 11 & 182\\ \hline 13& 219\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -1\\ \hline 2 & 17\\ \hline 11 & 179\\ \hline 13& 215\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -1\\ \hline 2 & 17\\ \hline 11 & 179\\ \hline 13& 215\\ \hline \end{tabular}}$

Explanation:

In the equation 18 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:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & 0\\ \hline 2 & 19\\ \hline 11 & 182\\ \hline 13& 219\\ \hline \end{tabular}}$

{18(1)+-19=0}

{18+-19=0}

${-1\neq 0}$

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

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 9 & 143\\ \hline 11 & 358\\ \hline 17 & 574\\ \hline 18& 610\\ \hline \end{tabular}}$

{18(9)-19=143}

{162-19=143}

{143=143}

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)-19=358}

{198-19=358}

${179\neq 358}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & 71\\ \hline 11 & 179\\ \hline 16 & 280\\ \hline 17& 297\\ \hline \end{tabular}}$

{18(5)-19=71}

{90-19=71}

{71=71}

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)-19=179}

{198-19=179}

{179=179}

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(16)-19=280}

{288-19=280}

${269\neq 280}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & 17\\ \hline 9 & 143\\ \hline 11 & 179\\ \hline 15& 251\\ \hline \end{tabular}}$

{18(2)-19=17}

{36-19=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.

{18(9)-19=143}

{162-19=143}

{143=143}

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)-19=179}

{198-19=179}

{179=179}

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(15)-19=251}

{270+-19=251}

{251=251}

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

Report an Error

Example Question #9 : 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 + 14 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & -81\\ \hline 14 & -252\\ \hline 15 & -260\\ \hline 17& -299\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -62\\ \hline 8 & -276\\ \hline 14 & -504\\ \hline 15& -542\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -62\\ \hline 8 & -138\\ \hline 14 & -252\\ \hline 15& -271\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -61\\ \hline 8 & -136\\ \hline 14 & -249\\ \hline 15& -267\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -62\\ \hline 8 & -138\\ \hline 14 & -252\\ \hline 15& -271\\ \hline \end{tabular}}$

Explanation:

In the equation - 19 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:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -61\\ \hline 8 & -136\\ \hline 14 & -249\\ \hline 15& -267\\ \hline \end{tabular}}$

{-19(4)+14=-61}

{-76+14=-61}

${-62\neq -61}$

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

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 7 & -119\\ \hline 13 & -466\\ \hline 14 & -504\\ \hline 18& -656\\ \hline \end{tabular}}$

{-19(7)+14=-119}

{-133+14=-119}

{-119=-119}

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(13)+14=-466}

{-247+14=-466}

${-233\neq -466}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 5 & -81\\ \hline 14 & -252\\ \hline 15 & -260\\ \hline 17& -309\\ \hline \end{tabular}}$

{-19(5)+14=-81}

{-95+14=-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.

{-19(14)+14=-252}

{-266+14=-252}

{-252=-252}

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(15)+14=-260}

{-285+14=-260}

${-271\neq -260}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & 14\\ \hline 3 & -43\\ \hline 5 & -81\\ \hline 17& -309\\ \hline \end{tabular}}$

{-19(0)+14=14}

{0+14=14}

{14=14}

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(3)+14=-43}

{-57+14=-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(5)+14=-81}

{-95+14=-81}

{-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.

{-19(17)+14=-309}

{-323+14=-309}

{-309=-309}

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

Report an Error

Example Question #10 : 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 - 3 = n

Possible Answers:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -55\\ \hline 13 & -344\\ \hline 17 & -448\\ \hline 18& -474\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -55\\ \hline 13 & -172\\ \hline 17 & -224\\ \hline 18& -237\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -3\\ \hline 2 & -29\\ \hline 9 & -109\\ \hline 18& -227\\ \hline \end{tabular}}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -54\\ \hline 13 & -170\\ \hline 17 & -221\\ \hline 18& -233\\ \hline \end{tabular}}$

Correct answer:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -55\\ \hline 13 & -172\\ \hline 17 & -224\\ \hline 18& -237\\ \hline \end{tabular}}$

Explanation:

In the equation - 13 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:

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 4 & -54\\ \hline 13 & -170\\ \hline 17 & -221\\ \hline 18& -233\\ \hline \end{tabular}}$

{-13(4)+-3=-54}

{-52+-3=-54}

${-55\neq -54}$

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

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 1 & -16\\ \hline 10 & -266\\ \hline 17 & -448\\ \hline 18& -474\\ \hline \end{tabular}}$

{-13(1)-3=-16}

{-13-3=-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.

{-13(10)-3=-266}

{-130-3=-266}

${-133\neq -266}$

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 0 & -3\\ \hline 2 & -29\\ \hline 9 & -109\\ \hline 18& -227\\ \hline \end{tabular}}$

{-13(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.

{-13(2)-3=-29}

{-26-3=-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.

{-13(9)-3=-109}

{-117-3=-109}

${-120\neq -109}$

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

${\begin{tabular}{|c|c|}\hline m & n \\ \hline 2 & -29\\ \hline 9 & -120\\ \hline 12 & -159\\ \hline 15& -198\\ \hline \end{tabular}}$

{-13(2)-3=-29}

{-26-3=-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.

{-13(9)-3=-120}

{-117-3=-120}

{-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.

{-13(12)-3=-159}

{-156-3=-159}

{-159=-159}

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(15)-3=-198}

{-195+-3=-198}

{-198=-198}

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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