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Common Core: 8th Grade Math : Expressions & Equations

Study concepts, example questions & explanations for Common Core: 8th Grade Math

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All Common Core: 8th Grade Math Resources

7 Diagnostic Tests 75 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #81 : Expressions & Equations

Select the graph that has a unit rate of

Possible Answers:

Graph C

Screen shot 2016 03 08 at 2.32.23 pm

Graph A

Screen shot 2016 03 08 at 2.14.15 pm

Graph D

Screen shot 2016 03 08 at 2.35.35 pm

Graph B

Screen shot 2016 03 08 at 2.11.02 pm

Correct answer:

Graph B

Screen shot 2016 03 08 at 2.11.02 pm

Explanation:

The unit rate of a graph is the slope of the graph. To solve for the slope we can use the following formula:

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Based on our formula, we first need to find two points for each of the graphs, and then we can solve for the slope.

Graph A

Points: (1,5) and (2,7)

Slope: $\frac{7-5}{2-1}=\frac{2}{1}=2$

Graph B

Points: (1,8) and (2,13)

Slope: $\frac{13-8}{2-1}=\frac{5}{1}=5$

Graph C

Points: (1,8) and (2,12)

Slope: $\frac{12-8}{2-1}=\frac{4}{1}=4$

Graph D

Points: (1,6) and (2,9)

Slope: $\frac{9-6}{2-1}=\frac{3}{1}=3$

We are looking for the graph with a slope, or unit rate, of ; thus, our correct answer is Graph B.

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Example Question #13 : Graph Proportional Relationships, Interpreting The Unit Rate As The Slope: Ccss.Math.Content.8.Ee.B.5

Select the graph with the lowest unit rate.

Possible Answers:

Graph D

Screen shot 2016 03 08 at 2.35.35 pm

Graph B

Screen shot 2016 03 08 at 2.11.02 pm

Graph A

Screen shot 2016 03 08 at 2.14.15 pm

Graph C

Screen shot 2016 03 08 at 2.32.23 pm

Correct answer:

Graph A

Screen shot 2016 03 08 at 2.14.15 pm

Explanation:

The lowest unit rate means that the slope is the lowest. So, first wee ned to solve for our slopes.

To solve for the slope we can use the following formula:

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Based on our formula, we first need to find two points for each of the graphs, and then we can solve for the slope.

Graph A

Points: (1,5) and (2,7)

Slope: $\frac{7-5}{2-1}=\frac{2}{1}=2$

Graph B

Points: (1,8) and (2,13)

Slope: $\frac{13-8}{2-1}=\frac{5}{1}=5$

Graph C

Points: (1,8) and (2,12)

Slope: $\frac{12-8}{2-1}=\frac{4}{1}=4$

Graph D

Points: (1,6) and (2,9)

Slope: $\frac{9-6}{2-1}=\frac{3}{1}=3$

We are looking for the graph with the lowest slope, or unit rate; thus, our correct answer is Graph A.

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Example Question #81 : Expressions & Equations

Select the equation that shows the greatest unit rate.

Possible Answers:

$y=\frac{1}{2}x+4$

$y=\frac{1}{4}x+6$

$y=\frac{1}{5}x+7$

$y=\frac{1}{3}x+5$

Correct answer:

$y=\frac{1}{2}x+4$

Explanation:

Unit rate is the slope of an equation. The equations in our answer options are written in slope intercept form:

y=mx+b

is always the slope, and is the -intercept.

We are looking for the equation with the greatest unit rate, or slope. Based on our options $\frac{1}{2}$ is the greatest value of ; thus our correct answer is $y=\frac{1}{2}x+4$

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Example Question #84 : Expressions & Equations

Select the equation that shows the lowest unit rate.

Possible Answers:

$y=\frac{1}{5}x+7$

$y=\frac{1}{2}x+4$

$y=\frac{1}{3}x+5$

$y=\frac{1}{4}x+6$

Correct answer:

$y=\frac{1}{5}x+7$

Explanation:

Unit rate is the slope of an equation. The equations in our answer options are written in slope intercept form:

y=mx+b

is always the slope, and is the -intercept.

We are looking for the equation with the lowest unit rate, or slope. Based on our options $\frac{1}{5}$ is the lowest value of ; thus our correct answer is $y=\frac{1}{5}x+7$

Report an Error

Example Question #85 : Expressions & Equations

Select the equation that shows the greatest unit rate.

Possible Answers:

y=6x+3

y=7x+3

y=5x+3

y=4x+3

Correct answer:

y=7x+3

Explanation:

Unit rate is the slope of an equation. The equations in our answer options are written in slope intercept form:

y=mx+b

is always the slope, and is the -intercept.

We are looking for the equation with the greatest unit rate, or slope. Based on our options is the greatest value of ; thus our correct answer is y=7x+3

Report an Error

Example Question #121 : Grade 8

Select the equation that shows the lowest unit rate.

Possible Answers:

y=4x+3

y=5x+3

y=6x+3

y=7x+3

Correct answer:

y=4x+3

Explanation:

Unit rate is the slope of an equation. The equations in our answer options are written in slope intercept form:

y=mx+b

is always the slope, and is the -intercept.

We are looking for the equation with the lowest unit rate, or slope. Based on our options is the lowest value of ; thus our correct answer is y=4x+3

Report an Error

Example Question #81 : Expressions & Equations

Select the equation that shows the lowest unit rate.

Possible Answers:

y=9x+11

y=10x+13

y=8x+11

y=6x+21

Correct answer:

y=6x+21

Explanation:

Unit rate is the slope of an equation. The equations in our answer options are written in slope intercept form:

y=mx+b

is always the slope, and is the -intercept.

We are looking for the equation with the lowest unit rate, or slope. Based on our options is the lowest value of ; thus our correct answer is y=6x+21

Report an Error

Example Question #82 : Expressions & Equations

Select the equation that shows the greatest unit rate.

Possible Answers:

y=9x+11

y=8x+11

y=10x+13

y=6x+21

Correct answer:

y=10x+13

Explanation:

Unit rate is the slope of an equation. The equations in our answer options are written in slope intercept form:

y=mx+b

is always the slope, and is the -intercept.

We are looking for the equation with the greatest unit rate, or slope. Based on our options, is the greatest value of ; thus, our correct answer is y=10x+13

Report an Error

Example Question #83 : Expressions & Equations

Select the graph with the greatest unit rate.

Possible Answers:

Graph D

Screen shot 2016 03 08 at 2.35.35 pm

Graph B

Screen shot 2016 03 08 at 2.11.02 pm

Graph A

Screen shot 2016 03 08 at 2.14.15 pm

Graph C

Screen shot 2016 03 08 at 2.32.23 pm

Correct answer:

Graph B

Screen shot 2016 03 08 at 2.11.02 pm

Explanation:

The highest unit rate means that the slope is the highest. So, first we ned to solve for our slopes.

To solve for the slope we can use the following formula:

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Based on our formula, we first need to find two points for each of the graphs, and then we can solve for the slope.

Graph A

Points: (1,5) and (2,7)

Slope: $\frac{7-5}{2-1}=\frac{2}{1}=2$

Graph B

Points: (1,8) and (2,13)

Slope: $\frac{13-8}{2-1}=\frac{5}{1}=5$

Graph C

Points: (1,8) and (2,12)

Slope: $\frac{12-8}{2-1}=\frac{4}{1}=4$

Graph D

Points: (1,6) and (2,9)

Slope: $\frac{9-6}{2-1}=\frac{3}{1}=3$

We are looking for the graph with the greatest slope, or unit rate; thus, our correct answer is Graph B.

Report an Error

Example Question #251 : Geometry

A line has the equation 5x-9y=12 . What is the slope of this line?

Possible Answers:

$\frac{5}{9}$

$-\frac{4}{3}$

$\frac{9}{5}$

Correct answer:

$\frac{5}{9}$

Explanation:

You need to put the equation in y=mx+b form before you can easily find out its slope.

5x-9y=12

-9y=-5x+12

$y=\frac{5}{9}x-\frac{4}{3}$

Since $m=\frac{5}{9}$ , that must be the slope.

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All Common Core: 8th Grade Math Resources

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Common Core: 8th Grade Math : Expressions & Equations

Study concepts, example questions & explanations for Common Core: 8th Grade Math

All Common Core: 8th Grade Math Resources

Example Questions

Example Question #81 : Expressions & Equations

Example Question #13 : Graph Proportional Relationships, Interpreting The Unit Rate As The Slope: Ccss.Math.Content.8.Ee.B.5

Example Question #81 : Expressions & Equations

Example Question #84 : Expressions & Equations

Example Question #85 : Expressions & Equations

Example Question #121 : Grade 8

Example Question #81 : Expressions & Equations

Example Question #82 : Expressions & Equations

Example Question #83 : Expressions & Equations

Example Question #251 : Geometry

All Common Core: 8th Grade Math Resources

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