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SSAT Upper Level Math : How to find slope of a line

Study concepts, example questions & explanations for SSAT Upper Level Math

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Example Questions

Example Question #21 : Other Lines

One end of a board that is four feet long is on the ground. The other end is balanced on a box that is one foot tall, creating a slope. What is the slope of the board?

Possible Answers:

$1\frac{1}{4}$

$\frac{1}{4}$

Correct answer:

$\frac{1}{4}$

Explanation:

The slope of a line is equal to $\frac{rise}{run}$ .

Given that the box is one foot tall, the rise will be equal to "1."

Given that the board is four feet long, the run will be equal to "4."

Therefore, the slope is equal to $\frac{rise}{run}=\frac{1}{4}$ .

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Example Question #1 : How To Find Slope Of A Line

A line is given with the equation 3y-18x=21 . What is the slope of this line?

Possible Answers:

Correct answer:

Explanation:

To find the slope, put the equation in y=mx+b form.

3y-18x=21

3y=18x+21

y=6x+7

Since m=6 , that must be the slope of the line.

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Example Question #21 : Lines

A line has the equation 8x-7y=14 . What is the slope of the line?

Possible Answers:

$-\frac{7}{8}$

$\frac{8}{7}$

$\frac{7}{8}$

$-\frac{8}{7}$

Correct answer:

$\frac{8}{7}$

Explanation:

Change the equation into the more familiar y=mx+b form. The value of will be the slope.

8x-7y=14

7y=8x-14

$y=\frac{8}{7}x-2$

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Example Question #71 : Geometry

What is the slope of a line that passes through the points $(15, -2)\text{ and }(-16, 20)$ ?

Possible Answers:

$-\frac{31}{22}$

$\frac{22}{31}$

$-\frac{22}{31}$

$\frac{31}{22}$

Correct answer:

$-\frac{22}{31}$

Explanation:

Use the following formula to find the slope:

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

Plug in the given points to find the slope.

$Slope=\frac{20-(-2)}{-16-15}=-\frac{22}{31}$

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Example Question #3 : How To Find Slope Of A Line

Find the slope of the line that passes through the points $(-9, 2)\text{ and }(-2, -2)$

Possible Answers:

$-\frac{7}{4}$

$\frac{4}{7}$

$\frac{7}{4}$

$-\frac{4}{7}$

Correct answer:

$-\frac{4}{7}$

Explanation:

Use the following formula to find the slope:

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

$\text{Slope}=\frac{-2-2}{-2-(-9)}=-\frac{4}{7}$

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Example Question #1 : How To Find Slope Of A Line

Find the slope of the line that passes through the points $(-6, 2)\text{ and }(4,-4)$

Possible Answers:

$-\frac{3}{5}$

$\frac{3}{5}$

Correct answer:

$-\frac{3}{5}$

Explanation:

Use the following formula to find the slope:

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

$\text{Slope}=\frac{-4-2}{4-(-6)}=\frac{-6}{10}=-\frac{3}{5}$

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Example Question #5 : How To Find Slope Of A Line

Find the slope of the line that passes through the points $(1,1)\text{ and }(-8,6)$ .

Possible Answers:

$-\frac{5}{9}$

$\frac{5}{9}$

$-\frac{9}{5}$

$\frac{9}{5}$

Correct answer:

$-\frac{5}{9}$

Explanation:

Use the following formula to find the slope:

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

$\text{Slope}=\frac{6-1}{-8-1}=-\frac{5}{9}$

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

Find the slope of the line that passes through the points $(2, -3)\text{ and }(-3, -3)$

Possible Answers:

$\frac{5}{6}$

$\frac{6}{5}$

$\text{Undefined}$

Correct answer:

Explanation:

Use the following formula to find the slope:

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

$\text{Slope}=\frac{-3-(-3)}{-3-2}=\frac{0}{-5}=0$

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Example Question #8 : How To Find Slope Of A Line

Find the slope of the line that passes through the points $\left(\frac{1}{3}, -\frac{4}{5}\right)$ and $\left ( -6,10\right )$ .

Possible Answers:

$-\frac{162}{95}$

$-\frac{95}{162}$

$\frac{162}{95}$

$\frac{95}{162}$

Correct answer:

$-\frac{162}{95}$

Explanation:

Use the following formula to find the slope:

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

Plug in the given points to find the slope.

$\text{Slope}=\frac{10-(-\frac{4}{5})}{-6-\frac{1}{3}}=\frac{\frac{54}{5}}{-\frac{19}{3}}=-\frac{162}{95}$

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Example Question #7 : How To Find Slope Of A Line

A line goes passes through the points $\left(-\frac{1}{2}, 5\right)\text{ and }\left(\frac{3}{2}, -1\right)$ . What is the slope of this line?

Possible Answers:

$\frac{1}{2}$

$-\frac{1}{2}$

Correct answer:

Explanation:

Use the following formula to find the slope of a line:

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

The slope of this line would be

$\frac{-1-5}{\frac{3}{2}-(-\frac{1}{2})}=\frac{-6}{2}=-3$

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SSAT Upper Level Math : How to find slope of a line

Study concepts, example questions & explanations for SSAT Upper Level Math

All SSAT Upper Level Math Resources

Example Questions

Example Question #21 : Other Lines

Example Question #1 : How To Find Slope Of A Line

Example Question #21 : Lines

Example Question #71 : Geometry

Example Question #3 : How To Find Slope Of A Line

Example Question #1 : How To Find Slope Of A Line

Example Question #5 : How To Find Slope Of A Line

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

Example Question #8 : How To Find Slope Of A Line

Example Question #7 : How To Find Slope Of A Line

All SSAT Upper Level Math Resources

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