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Common Core: 8th Grade Math : Grade 8

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 #141 : Grade 8

Using the similar triangles, find the equation of the line in the provided graph.

Possible Answers:

y=4x+4

y=2x+4

y=6x+4

y=3x+4

Correct answer:

y=2x+4

Explanation:

The equation for a line can be written in the slope-intercept form:

y=mx+b ,

In this equation, the variables and are defined as the following:

$\textup{m=slope}$

$\textup{b=y-intercept}$

One way to find the slope of a line is to solve for the rise over run:

$\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}$

This is defined as the change in the y-axis over the change in the x axis.

$\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$

The triangles in the graph provide possess two different values for their respective rise over run calculations; however, both triangles should have the same slope:

$\frac{4}{2}=2$

$\frac{6}{3}=2$

Now that we've found the slope of our line, , we can look at the graph to see where the line crosses the y-axis. The line crosses the y-axis at the following point:

(0,4)

Therefore, the equation of this line is,

y=2x+4

Report an Error

Example Question #103 : Expressions & Equations

Using the similar triangles, find the equation of the line in the provided graph.

Possible Answers:

y=2x+1

y=x+2

y=3x+2

y=7x+2

Correct answer:

y=x+2

Explanation:

The equation for a line can be written in the slope-intercept form:

y=mx+b ,

In this equation, the variables and are defined as the following:

$\textup{m=slope}$

$\textup{b=y-intercept}$

One way to find the slope of a line is to solve for the rise over run:

$\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}$

This is defined as the change in the y-axis over the change in the x axis.

$\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$

The triangles in the graph provide possess two different values for their respective rise over run calculations; however, both triangle should have the same slope:

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

$\frac{7}{7}=1$

Now that we've found the slope of our line, , we can look at the graph to see where the line crosses the y-axis. The line crosses the y-axis at the following point:

(0,2)

Therefore, the equation of this line is,

y=x+2

Report an Error

Example Question #142 : Grade 8

Using the similar triangles, find the equation of the line in the provided graph.

Possible Answers:

y=4x

y=2x+0

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

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

Correct answer:

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

Explanation:

The equation for a line can be written in the slope-intercept form:

y=mx+b ,

In this equation, the variables and are defined as the following:

$\textup{m=slope}$

$\textup{b=y-intercept}$

One way to find the slope of a line is to solve for the rise over run:

$\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}$

This is defined as the change in the y-axis over the change in the x axis.

$\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$

The triangles in the graph provide possess two different values for their respective rise over run calculations; however, both triangle should have the same slope:

$\frac{2}{4}=\frac{1}{2}$

$\frac{3}{6}=\frac{1}{2}$

Now that we've found the slope of our line, $\frac{1}{2}$ , we can look at the graph to see where the line crosses the y-axis. The line crosses the y-axis at the following point:

(0,0)

Therefore, the equation of this line is,

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

Report an Error

Example Question #105 : Expressions & Equations

Using the similar triangles, find the equation of the line in the provided graph.

Possible Answers:

y=x+1

y=8x+1

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

y=2x

Correct answer:

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

Explanation:

The equation for a line can be written in the slope-intercept form:

y=mx+b ,

In this equation, the variables and are defined as the following:

$\textup{m=slope}$

$\textup{b=y-intercept}$

One way to find the slope of a line is to solve for the rise over run:

$\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}$

This is defined as the change in the y-axis over the change in the x axis.

$\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$

The triangles in the graph provide possess two different values for their respective rise over run calculations; however, both triangle should have the same slope:

$\frac{1}{2}=\frac{1}{2}$

$\frac{4}{8}=\frac{1}{2}$

Now that we've found the slope of our line, $\frac{1}{2}$ , we can look at the graph to see where the line crosses the y-axis. The line crosses the y-axis at the following point:

(0,1)

Therefore, the equation of this line is,

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

Report an Error

Example Question #106 : Expressions & Equations

Using the similar triangles, find the equation of the line in the provided graph.

Possible Answers:

y=3x+7

$y=\frac{1}{3}x+7$

y=2x+7

$y=\frac{1}{2}x+7$

Correct answer:

y=2x+7

Explanation:

The equation for a line can be written in the slope-intercept form:

y=mx+b ,

In this equation, the variables and are defined as the following:

$\textup{m=slope}$

$\textup{b=y-intercept}$

One way to find the slope of a line is to solve for the rise over run:

$\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}$

This is defined as the change in the y-axis over the change in the x axis.

$\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$

The triangles in the graph provide possess two different values for their respective rise over run calculations; however, both triangle should have the same slope:

$\frac{6}{3}=2$

$\frac{2}{1}=2$

Now that we've found the slope of our line, , we can look at the graph to see where the line crosses the y-axis. The line crosses the y-axis at the following point:

(0,7)

Therefore, the equation of this line is,

y=2x+7

Report an Error

Example Question #143 : Grade 8

Using the similar triangles, find the equation of the line in the provided graph.

Possible Answers:

$y=\frac{1}{3}x+4$

$y=\frac{1}{4}x+3$

y=4x+3

y=3x+4

Correct answer:

y=4x+3

Explanation:

The equation for a line can be written in the slope-intercept form:

y=mx+b ,

In this equation, the variables and are defined as the following:

$\textup{m=slope}$

$\textup{b=y-intercept}$

One way to find the slope of a line is to solve for the rise over run:

$\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}$

This is defined as the change in the y-axis over the change in the x axis.

$\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$

The triangles in the graph provide possess two different values for their respective rise over run calculations; however, both triangle should have the same slope:

$\frac{4}{1}=4$

$\frac{8}{2}=4$

Now that we've found the slope of our line, , we can look at the graph to see where the line crosses the y-axis. The line crosses the y-axis at the following point:

(0,3)

Therefore, the equation of this line is,

y=4x+3

Report an Error

Example Question #111 : Expressions & Equations

Using the similar triangles, find the equation of the line in the provided graph.

Possible Answers:

y=4x+1

y=4x+4

y=4x

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

Correct answer:

y=4x

Explanation:

The equation for a line can be written in the slope-intercept form:

y=mx+b ,

In this equation, the variables and are defined as the following:

$\textup{m=slope}$

$\textup{b=y-intercept}$

One way to find the slope of a line is to solve for the rise over run:

$\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}$

This is defined as the change in the y-axis over the change in the x axis.

$\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$

The triangles in the graph provide possess two different values for their respective rise over run calculations; however, both triangle should have the same slope:

$\frac{8}{2}=4$

$\frac{4}{1}=4$

Now that we've found the slope of our line, , we can look at the graph to see where the line crosses the y-axis. The line crosses the y-axis at the following point:

(0,0)

Therefore, the equation of this line is,

y=4x

Report an Error

Example Question #142 : Grade 8

Using the similar triangles, find the equation of the line in the provided graph.

Possible Answers:

y=3x

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

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

y=3x+1

Correct answer:

y=3x

Explanation:

The equation for a line can be written in the slope-intercept form:

y=mx+b ,

In this equation, the variables and are defined as the following:

$\textup{m=slope}$

$\textup{b=y-intercept}$

One way to find the slope of a line is to solve for the rise over run:

$\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}$

This is defined as the change in the y-axis over the change in the x axis.

$\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$

The triangles in the graph provide possess two different values for their respective rise over run calculations; however, both triangle should have the same slope:

$\frac{9}{3}=3$

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

Now that we've found the slope of our line, , we can look at the graph to see where the line crosses the y-axis. The line crosses the y-axis at the following point:

(0,0)

Therefore, the equation of this line is,

y=3x

Report an Error

Example Question #24 : Use Similar Triangles To Show Equal Slopes: Ccss.Math.Content.8.Ee.B.6

Using the similar triangles, find the equation of the line in the provided graph.

Possible Answers:

$y=\frac{1}{2}x+3$

y=3x+2

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

y=2x+3

Correct answer:

y=3x+2

Explanation:

The equation for a line can be written in the slope-intercept form:

y=mx+b ,

In this equation, the variables and are defined as the following:

$\textup{m=slope}$

$\textup{b=y-intercept}$

One way to find the slope of a line is to solve for the rise over run:

$\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}$

This is defined as the change in the y-axis over the change in the x axis.

$\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$

The triangles in the graph provide possess two different values for their respective rise over run calculations; however, both triangle should have the same slope:

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

$\frac{6}{2}=3$

Now that we've found the slope of our line, , we can look at the graph to see where the line crosses the y-axis. The line crosses the y-axis at the following point:

(0,2)

Therefore, the equation of this line is,

y=3x+2

Report an Error

Example Question #143 : Grade 8

Using the similar triangles, find the equation of the line in the provided graph.

Possible Answers:

y=5x+1

y=x+5

$y=\frac{5}{8}x+5$

y=3x+5

Correct answer:

y=x+5

Explanation:

The equation for a line can be written in the slope-intercept form:

y=mx+b ,

In this equation, the variables and are defined as the following:

$\textup{m=slope}$

$\textup{b=y-intercept}$

One way to find the slope of a line is to solve for the rise over run:

$\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}$

This is defined as the change in the y-axis over the change in the x axis.

$\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$

The triangles in the graph provide possess two different values for their respective rise over run calculations; however, both triangle should have the same slope:

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

$\frac{5}{5}=1$

Now that we've found the slope of our line, , we can look at the graph to see where the line crosses the y-axis. The line crosses the y-axis at the following point:

(0,5)

Therefore, the equation of this line is,

y=x+5

Report an Error

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All Common Core: 8th Grade Math Resources

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Common Core: 8th Grade Math : Grade 8

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

All Common Core: 8th Grade Math Resources

Example Questions

Example Question #141 : Grade 8

Example Question #103 : Expressions & Equations

Example Question #142 : Grade 8

Example Question #105 : Expressions & Equations

Example Question #106 : Expressions & Equations

Example Question #143 : Grade 8

Example Question #111 : Expressions & Equations

Example Question #142 : Grade 8

Example Question #24 : Use Similar Triangles To Show Equal Slopes: Ccss.Math.Content.8.Ee.B.6

Example Question #143 : Grade 8

All Common Core: 8th Grade Math Resources

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