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Algebra 1 : Functions and Lines

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #14 : How To Find The Slope Of Perpendicular Lines

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

$y=\frac{1}{3}x-9$

Possible Answers:

$\frac{1}{3}$

$-\frac{1}{3}$

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 $\frac{1}{3}$ .

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

Next, change the sign.

$3\rightarrow-3$

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Example Question #44 : Perpendicular Lines

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

y=2x-2

Possible Answers:

$\frac{1}{2}$

$-\frac{1}{2}$

Correct answer:

$-\frac{1}{2}$

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 :

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

Flip the numerator and the denominator.

$\frac{2}{1}\rightarrow \frac{1}{2}$

Next, change the sign.

$\frac{1}{2}\rightarrow-\frac{1}{2}$

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Example Question #45 : Perpendicular Lines

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

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

Possible Answers:

$\frac{2}{3}$

$-\frac{2}{3}$

$-\frac{3}{2}$

$\frac{3}{2}$

Correct answer:

$\frac{3}{2}$

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 $-\frac{2}{3}$ .

$-\frac{2}{3}\rightarrow-\frac{3}{2}$

Next, change the sign.

$-\frac{3}{2}\rightarrow\frac{3}{2}$

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Example Question #15 : How To Find The Slope Of Perpendicular Lines

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

y=-10x+9

Possible Answers:

$-\frac{1}{10}$

$\frac{1}{10}$

Correct answer:

$\frac{1}{10}$

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 .

$-10=-\frac{10}{1}$

Flip the numerator and the denominator.

$-\frac{10}{1}=-\frac{1}{10}$

Next, change the sign.

$-\frac{1}{10}\rightarrow\frac{1}{10}$

Report an Error

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:

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

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.

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 #21 : How To Find The Slope Of Perpendicular 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.

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

Report an Error

Example Question #22 : 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:

$-\frac{7}{3}$

$\frac{3}{7}$

$\frac{7}{3}$

$-\frac{3}{7}$

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.

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

Report an Error

Example Question #23 : How To Find The Slope Of Perpendicular Lines

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

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

Possible Answers:

$-\frac{2}{5}$

$\frac{5}{2}$

$-\frac{5}{2}$

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 #24 : How To Find The Slope Of Perpendicular 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:

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

y=-5x-2

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

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 #25 : How To Find The Slope Of Perpendicular 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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Algebra 1 : Functions and Lines

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #14 : How To Find The Slope Of Perpendicular Lines

Example Question #44 : Perpendicular Lines

Example Question #45 : Perpendicular Lines

Example Question #15 : How To Find The Slope Of Perpendicular Lines

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

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

Example Question #22 : How To Find The Slope Of Perpendicular Lines

Example Question #23 : How To Find The Slope Of Perpendicular Lines

Example Question #24 : How To Find The Slope Of Perpendicular Lines

Example Question #25 : How To Find The Slope Of Perpendicular Lines

All Algebra 1 Resources

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