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

A line crosses the x-axis at (6,8) and the y-axis at (0,6) . What is the slope of this line?

Possible Answers:

None of these.

m=3

$m=-\frac{1}{3}$

m=-3

$m=\frac{1}{3}$

Correct answer:

$m=\frac{1}{3}$

Explanation:

Given the points,

$\\(x_1,y_1)=(0,6) \\(x_2,y_2)=(6,8)$ .

We compute slope (m) as follows:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{8-6}{6-0}=\mathbf{\frac{1}{3}}$

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Example Question #1423 : Intermediate Geometry

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

(12, 2) and (-12, 4)

Possible Answers:

$-\frac{3}{4}$

$-\frac{1}{12}$

Correct answer:

$-\frac{1}{12}$

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.

$\text{Slope}=\frac{4-2}{-12-12}$

Simplify.

$\text{Slope}=\frac{2}{-24}$

Solve.

$\text{Slope}=-\frac{1}{12}$

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Example Question #1424 : Intermediate Geometry

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

(2, 4) and (-10, -20)

Possible Answers:

$-\frac{1}{2}$

$\frac{7}{8}$

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.

$\text{Slope}=\frac{-20-4}{-10-2}$

Simplify.

$\text{Slope}=\frac{-24}{-12}$

Solve.

$\text{Slope}=2$

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Example Question #2 : How To Find The Slope Of A Line

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

(4, 5) and (-3, 1)

Possible Answers:

$-\frac{2}{7}$

$\frac{4}{7}$

$\frac{3}{7}$

$\frac{5}{7}$

Correct answer:

$\frac{4}{7}$

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.

$\text{Slope}=\frac{1-5}{-3-4}$

Simplify.

$\text{Slope}=\frac{-4}{-7}$

Solve.

$\text{Slope}=\frac{4}{7}$

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Example Question #1426 : Intermediate Geometry

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

(8, 15) and (-39, 13)

Possible Answers:

$\frac{19}{4}$

$\frac{2}{47}$

$\frac{12}{47}$

$-\frac{34}{47}$

Correct answer:

$\frac{2}{47}$

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.

$\text{Slope}=\frac{13-15}{-39-8}$

Simplify.

$\text{Slope}=\frac{-2}{-47}$

Solve.

$\text{Slope}=\frac{2}{47}$

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

Example Question #1423 : Intermediate Geometry

Example Question #1424 : Intermediate Geometry

Example Question #2 : How To Find The Slope Of A Line

Example Question #1426 : Intermediate Geometry

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

All Common Core: 8th Grade Math Resources

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