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Common Core: 8th Grade Math : Graph Proportional Relationships, Interpreting the Unit Rate as the Slope: CCSS.Math.Content.8.EE.B.5

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

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All Common Core: 8th Grade Math Resources

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Example Questions

Example Question #1427 : Intermediate Geometry

Find the slope of the line that passes through the points:

(4, -10) and (5, 6)

Possible Answers:

Correct answer:

Explanation:

Recall that the slope of a line also measures how steep the line is. Use the following equation to find the slope of the line:

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

Now, substitute in the information using the given points.

$\text{Slope}=\frac{6-(-10)}{5-4}$

Simplify.

$\text{Slope}=\frac{16}{1}$

Solve.

$\text{Slope}=16$

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Example Question #11 : Graph Proportional Relationships, Interpreting The Unit Rate As The Slope: Ccss.Math.Content.8.Ee.B.5

What is the slope m of the line below?

y - 2= 2(x-4)

Possible Answers:

m = 2

m=4

m=-2

m=-4

m=-8

Correct answer:

m = 2

Explanation:

To answer this question you should realize that the equation for the line is given in point - slope form. The standard point slope form of a line is given below:

y-y_1 = m(x-x_1)

m represents the slope of the line so all we have to do is recognize the correct line form and we automatically know that the slope is m = 2

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Example Question #111 : Grade 8

Select the graph that has a unit rate of

Possible Answers:

Graph D

Screen shot 2016 03 08 at 2.35.35 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

Graph B

Screen shot 2016 03 08 at 2.11.02 pm

Correct answer:

Graph A

Screen shot 2016 03 08 at 2.14.15 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 graph, 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 A.

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Example Question #12 : Graph Proportional Relationships, Interpreting The Unit Rate As The Slope: Ccss.Math.Content.8.Ee.B.5

Select the graph that has a unit rate of

Possible Answers:

Graph B

Screen shot 2016 03 08 at 2.11.02 pm

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

Correct answer:

Graph D

Screen shot 2016 03 08 at 2.35.35 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 D.

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Example Question #11 : Graph Proportional Relationships, Interpreting The Unit Rate As The Slope: Ccss.Math.Content.8.Ee.B.5

Select the graph that has a unit rate of

Possible Answers:

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

Graph C

Screen shot 2016 03 08 at 2.32.23 pm

Correct answer:

Graph C

Screen shot 2016 03 08 at 2.32.23 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 C.

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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.

Report an Error

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.

Report an Error

Example Question #11 : Graph Proportional Relationships, Interpreting The Unit Rate As The Slope: Ccss.Math.Content.8.Ee.B.5

Select the equation that shows the greatest unit rate.

Possible Answers:

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

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

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

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

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

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Common Core: 8th Grade Math : Graph Proportional Relationships, Interpreting the Unit Rate as the Slope: CCSS.Math.Content.8.EE.B.5

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

All Common Core: 8th Grade Math Resources

Example Questions

Example Question #1427 : Intermediate Geometry

Example Question #11 : Graph Proportional Relationships, Interpreting The Unit Rate As The Slope: Ccss.Math.Content.8.Ee.B.5

Example Question #111 : Grade 8

Example Question #12 : Graph Proportional Relationships, Interpreting The Unit Rate As The Slope: Ccss.Math.Content.8.Ee.B.5

Example Question #11 : Graph Proportional Relationships, Interpreting The Unit Rate As The Slope: Ccss.Math.Content.8.Ee.B.5

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

Example Question #84 : Expressions & Equations

Example Question #85 : Expressions & Equations

All Common Core: 8th Grade Math Resources

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