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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 #121 : Grade 8

Select the equation that shows the greatest unit rate.

Possible Answers:

y=6x+3

y=4x+3

y=5x+3

y=7x+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

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Example Question #21 : Graph Proportional Relationships, Interpreting The Unit Rate As The Slope: Ccss.Math.Content.8.Ee.B.5

Select the equation that shows the lowest unit rate.

Possible Answers:

y=7x+3

y=4x+3

y=6x+3

y=5x+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

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Example Question #121 : Grade 8

Select the equation that shows the lowest unit rate.

Possible Answers:

y=10x+13

y=8x+11

y=9x+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

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Example Question #121 : Grade 8

Select the equation that shows the greatest unit rate.

Possible Answers:

y=10x+13

y=9x+11

y=8x+11

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 #122 : Grade 8

Select the graph with the greatest unit rate.

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 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.

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Example Question #1 : Slope

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

Possible Answers:

$\frac{9}{5}$

$\frac{5}{9}$

$-\frac{4}{3}$

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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Example Question #1 : How To Find Slope

The equation of a line is 12x-8y=6 . Find the slope of this line.

Possible Answers:

$-\frac{3}{2}$

$\frac{3}{4}$

$-\frac{3}{4}$

$\frac{3}{2}$

Correct answer:

$\frac{3}{2}$

Explanation:

To find the slope, you will need to put the equation in y=mx+b form. The value of will be the slope.

12x-8y=6

Subtract from either side:

8y=12x-6

Divide each side by :

$y=\frac{3}{2}x-\frac{3}{4}$

You can now easily identify the value of .

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

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Example Question #297 : Geometry

What is the -intercept of the graph of the function $f \left ( x\right ) = 2x^{2} - 7x + 5$ ?

Possible Answers:

$\left (0,-7 \right )$

$\left (0,5 \right )$

$\left (0,0 \right )$

$\left (0,2 \right )$

$\left ( 0, -3 \frac{1}{2}\right )$

Correct answer:

$\left (0,5 \right )$

Explanation:

The -intercept of the graph of a function is the point at which it intersects the -axis - that is, at which x = 0 . This point is $\left (0, f(0) \right )$ , so evaluate f(0) :

$f \left ( x\right ) = 2x^{2} - 7x + 5$

$f \left (0\right ) = 2 \cdot 0^{2} - 7 \cdot 0 + 5$

$f \left (0\right ) = 0- 0 + 5 = 5$

The -intercept is $\left (0,5 \right )$ .

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Example Question #123 : Grade 8

Give the -intercept, if there is one, of the graph of the equation

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

Possible Answers:

$\left ( 0, \frac{3}{2}\right )$

(0,4)

The graph has no -intercept.

(0,3)

(0,2)

Correct answer:

The graph has no -intercept.

Explanation:

The -intercept is the point at which the graph crosses the -axis; at this point, the -coordinate is 0, so substitute for in the equation:

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

$y = \frac{1}{0^{2}+0} + 3$

$y = \frac{1}{0} + 3$

However, since this expression has 0 in a denominator, it is of undefined value. This means that there is no value of paired with -coordinate 0, and, subsequently, the graph of the equation has no -intercept.

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Example Question #124 : Grade 8

Give the -intercept, if there is one, of the graph of the equation

$y = \frac{3}{\left | 3x-8\right |}$

Possible Answers:

$\left ( 0, -\frac{3}{8}\right )$

$\left ( 0,- \frac{3}{5}\right )$

$\left ( 0, \frac{3}{8}\right )$

$\left ( 0, \frac{3}{5}\right )$

The graph has no -intercept.

Correct answer:

$\left ( 0, \frac{3}{8}\right )$

Explanation:

The -intercept is the point at which the graph crosses the -axis; at this point, the -coordinate is 0, so substitute for in the equation:

$y = \frac{3}{\left | 3x-8\right |}$

$y = \frac{3}{\left | 3 \cdot 0 -8\right |}$

$y = \frac{3}{\left | 0 -8\right |}$

$y = \frac{3}{\left | -8\right |}$

$y = \frac{3}{ 8}$

The -intercept is $\left ( 0, \frac{3}{8}\right )$ .

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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 #121 : Grade 8

Example Question #21 : Graph Proportional Relationships, Interpreting The Unit Rate As The Slope: Ccss.Math.Content.8.Ee.B.5

Example Question #121 : Grade 8

Example Question #121 : Grade 8

Example Question #122 : Grade 8

Example Question #1 : Slope

Example Question #1 : How To Find Slope

Example Question #297 : Geometry

Example Question #123 : Grade 8

Example Question #124 : Grade 8

All Common Core: 8th Grade Math Resources

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