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Algebra 1 : How to find the slope of perpendicular lines

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Example Question #41 : Perpendicular Lines

Find the slope of a line that is perpendicular to a line with the equation:

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

Possible Answers:

$-\frac{1}{4}$

$\frac{1}{4}$

Correct answer:

Explanation:

Lines can be written in the slope-intercept form:

y=mx+b

In this equation, is the slope and is the y-intercept.

Lines that are perpendicular to each other have slopes that are negative reciprocals of each other. This means that you need to flip the numerator and denominator of the given slope and then change the sign.

First, find the reciprocal of $\frac{1}{4}$ .

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

Next, change the sign.

$4\rightarrow-4$

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Example Question #51 : Equations Of Lines

Find the slope of the line that is perpendicular to a line with the equation:

y=-8x-2

Possible Answers:

$-\frac{1}{8}$

$\frac{1}{8}$

Correct answer:

$\frac{1}{8}$

Explanation:

Lines can be written in the slope-intercept form:

y=mx+b

In this equation, is the slope and is the y-intercept.

First, find the reciprocal of .

$-8=-\frac{8}{1}$

Flip the numerator and the denominator.

$-\frac{8}{1}\rightarrow-\frac{1}{8}$

Next, change the sign.

$-\frac{1}{8}\rightarrow \frac{1}{8}$

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Example Question #21 : How To Find The Slope Of Perpendicular Lines

Find the slope of a line that is perpendicular to a line with the equation:

$y=\frac{3}{7}x-2$

Possible Answers:

$\frac{7}{3}$

$\frac{3}{7}$

$-\frac{3}{7}$

$-\frac{7}{3}$

Correct answer:

$-\frac{7}{3}$

Explanation:

Lines can be written in the slope-intercept form:

y=mx+b

In this equation, is the slope and is the y-intercept.

First, find the reciprocal of $\frac{3}{7}$ .

$\frac{3}{7}\rightarrow \frac{7}{3}$

Next, change the sign.

$\frac{7}{3}\rightarrow -\frac{7}{3}$

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Example Question #53 : Equations Of Lines

Find the slope of a line that is perpendicular to a line with the equation:

$y=-\frac{2}{5}x+2$

Possible Answers:

$\frac{5}{2}$

$-\frac{2}{5}$

$-\frac{5}{2}$

Correct answer:

$\frac{5}{2}$

Explanation:

Lines can be written in the slope-intercept form:

y=mx+b

In this equation, is the slope and is the y-intercept.

First, find the reciprocal of $-\frac{2}{5}$ .

$-\frac{2}{5}\rightarrow-\frac{5}{2}$

Next, change the sign.

$-\frac{5}{2}\rightarrow \frac{5}{2}$

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Example Question #54 : Equations Of Lines

Two lines intersect at the point (5,1) . Which of the following lines is perpendicular to a line with the equation:

y=-5x+2

Possible Answers:

$y=-\frac{1}{5}x-1$

y=-5x-2

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

y=5x+2

Correct answer:

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

Explanation:

Lines can be written in the slope-intercept form:

y=mx+b

In this equation, is the slope and is the y-intercept.

First, find the reciprocal of .

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

Flip the numerator and the denominator.

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

Next, change the sign.

$-\frac{1}{5}\rightarrow \frac{1}{5}$

Substitute this new slope into the position of the point-slope formula:

$y-y_{1}=\frac{1}{5}(x-x_{1})$

Insert the point (5,1) into the $x_{1}$ and $y_{1}$ variables of the point-slope equation. Remember that points are written in the format: (x,y) .

$y-1=\frac{1}{5}(x-5)$

Simplify to find the equation of the line in slope-intercept form.

Distribute.

$y-1=\frac{1}{5}(x)-\frac{1}{5}(5)$

Simplify.

$y-1=\frac{1}{5}(x)-\frac{1}{5}\left ( \frac{5}{1} \right )$

$y-1=\frac{1}{5}x-1$

Add to both sides.

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

Simplify

$y=\frac{1}{5}x+0$

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

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Example Question #55 : Equations Of Lines

Find the slope of a line that is perpendicular to a line with the equation y=-x+2 .

Possible Answers:

Correct answer:

Explanation:

Lines can be written in the slope-intercept form:

y=mx+b

In this equation, is the slope and is the y-intercept.

The reciprocal of is ; therefore, the reciprocal of is .

Next, change the sign.

$-1\rightarrow 1$

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Example Question #56 : Equations Of Lines

Find the slope of a line that is perpendicular to a line with the equation:

$y=\frac{4}{5}x-5$

Possible Answers:

$\frac{4}{5}$

$-\frac{4}{5}$

$-\frac{5}{4}$

$\frac{5}{4}$

Correct answer:

$-\frac{5}{4}$

Explanation:

Lines can be written in the slope-intercept form:

y=mx+b

In this equation, is the slope and is the y-intercept.

First, find the reciprocal of $\frac{4}{5}$ .

$\frac{4}{5}\rightarrow \frac{5}{4}$

Next, change the sign.

$\frac{5}{4}\rightarrow -\frac{5}{4}$

Report an Error

Example Question #57 : Equations Of Lines

Find the slope of a line that is perpendicular to a line with the equation:

y=-6x+2

Possible Answers:

$\frac{1}{6}$

$-\frac{1}{6}$

Correct answer:

$\frac{1}{6}$

Explanation:

Lines can be written in the slope-intercept form:

y=mx+b

In this equation, is the slope and is the y-intercept.

First, find the reciprocal of .

$-6=-\frac{6}{1}$

Flip the numerator and the denominator.

$-\frac{6}{1}=-\frac{1}{6}$

Next, change the sign.

$-\frac{1}{6}\rightarrow \frac{1}{6}$

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Example Question #58 : Equations Of Lines

A line with a y-intercept of $\small -1$ is perpendicular to another line with a slope of . Find the slope of the perpendicular line.

Possible Answers:

$\small - \frac{1}{3}$

$\frac{2}{3}$

$\small \frac{1}{3}$

Correct answer:

$\small \frac{1}{3}$

Explanation:

This problem can be easily solved for by remembering what defines a perpendicular line. A line is perpendicular to another when the product of the two lines' slope is -1. For instance, if a line has a slope of $\small 2$ , the line perpendicular to it will have a slope of $\small -\frac{1}2$ because $\small 2 \cdot -\frac{1}{2}=-1$ . Using this example, if the reference line has a slope of , that means the line of interest must have a slope of $+\frac{1}{3}$ . The product of these two numbers is .

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Example Question #59 : Equations Of Lines

A line is perpendicular to $y=-\frac{1}{7}x+34$ . What is the slope of the perpendicular line?

Possible Answers:

$-\frac{1}{7}$

$\frac{1}{7}$

Correct answer:

Explanation:

This problem can be easily solved for by remembering what defines a perpendicular line. A line is perpendicular to another when the product of the two lines' slope is -1.

For instance, if a line has a slope of $\small 2$ , the line perpendicular to it will have a slope of $\small -\frac{1}2$ because $\small 2 \cdot -\frac{1}{2}=-1$ .

Using this example, if the reference line has a slope of $-\frac{1}{7}$ , that means the line of interest must have a slope of .

The product of these two numbers is .

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Algebra 1 : How to find the slope of perpendicular lines

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #41 : Perpendicular Lines

Example Question #51 : Equations Of Lines

Example Question #21 : How To Find The Slope Of Perpendicular Lines

Example Question #53 : Equations Of Lines

Example Question #54 : Equations Of Lines

Example Question #55 : Equations Of Lines

Example Question #56 : Equations Of Lines

Example Question #57 : Equations Of Lines

Example Question #58 : Equations Of Lines

Example Question #59 : Equations Of Lines

All Algebra 1 Resources

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