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Algebra 1 : Equations of Lines

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Example Questions

Example Question #11 : Perpendicular Lines

Find a line perpendicular to the line with the equation:

$y=\frac{7}{9}x-1$

Possible Answers:

$y=\frac{7}{9}x+6$

$y=-\frac{9}{7}x+9$

$y=\frac{9}{7}x+15$

$y=-\frac{7}{9}x-8$

Correct answer:

$y=-\frac{9}{7}x+9$

Explanation:

Lines can be written in the slope-intercept format:

y=mx+b

In this format, equals the line's slope and represents where the line intercepts the y-axis.

In the given equation:

$m=\frac{7}{9}$

Perpendicular lines have slopes that are negative reciprocals of each other.

First, we need to find its reciprocal.

$\frac{7}{9}\rightarrow\frac{9}{7}$

Second, we need to rewrite it with the opposite sign.

$\frac{9}{7}\rightarrow-\frac{9}{7}$

Only one of the choices has a slope of $-\frac{9}{7}$ .

$y=-\frac{9}{7}x+9$

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Example Question #12 : Perpendicular Lines

Find a line perpendicular to the line with the equation:

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

Possible Answers:

y=-5x-7

$y=-\frac{2}{5}x+9$

$y=\frac{2}{5}x+1$

$y=\frac{5}{2}x-8$

Correct answer:

$y=-\frac{2}{5}x+9$

Explanation:

Lines can be written in the slope-intercept format:

y=mx+b

In this format, equals the line's slope and represents where the line intercepts the y-axis.

In the given equation:

$m=\frac{5}{2}$

Perpendicular lines have slopes that are negative reciprocals of each other.

First, we need to find its reciprocal.

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

Second, we need to rewrite it with the opposite sign.

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

Only one of the choices has a slope of $-\frac{2}{5}$ .

$y=-\frac{2}{5}x+9$

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Example Question #13 : Perpendicular Lines

Find a line perpendicular to the line with the equation:

$y=-\frac{5}{7}x-61$

Possible Answers:

$y=\frac{7}{5}x+159$

$y=-\frac{7}{5}x-78$

$y=\frac{7}{6}x+78$

$y=\frac{5}{7}x+97$

Correct answer:

$y=\frac{7}{5}x+159$

Explanation:

Lines can be written in the slope-intercept format:

y=mx+b

In this format, equals the line's slope and represents where the line intercepts the y-axis.

In the given equation:

$m=-\frac{5}{7}$

Perpendicular lines have slopes that are negative reciprocals of each other.

First, we need to find its reciprocal.

$-\frac{5}{7}\rightarrow-\frac{7}{5}$

Second, we need to rewrite it with the opposite sign.

$-\frac{7}{5}\rightarrow\frac{7}{5}$

Only one of the choices has a slope of $\frac{7}{5}$ .

$y=\frac{7}{5}x+159$

Report an Error

Example Question #14 : Perpendicular Lines

Find a line perpendicular to the line with the equation:

$y=\frac{3}{4}x-23$

Possible Answers:

$y=-\frac{3}{4}x+84$

$y=\frac{4}{3}x-88$

$y=\frac{3}{4}x+56$

$y=-\frac{4}{3}x+87$

Correct answer:

$y=-\frac{4}{3}x+87$

Explanation:

Lines can be written in the slope-intercept format:

y=mx+b

In this format, equals the line's slope and represents where the line intercepts the y-axis.

In the given equation:

$m=\frac{3}{4}$

Perpendicular lines have slopes that are negative reciprocals of each other.

First, we need to find its reciprocal.

$\frac{3}{4}\rightarrow\frac{4}{3}$

Second, we need to rewrite it with the opposite sign.

$\frac{4}{3}\rightarrow-\frac{4}{3}$

Only one of the choices has a slope of $-\frac{4}{3}$ .

$y=-\frac{4}{3}x+87$

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Example Question #15 : Perpendicular Lines

Find a line perpendicular to the line with the equation:

y=2x-10

Possible Answers:

y=-2x+2

y=2x+2

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

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

Correct answer:

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

Explanation:

Lines can be written in the slope-intercept format:

y=mx+b

In this format, equals the line's slope and represents where the line intercepts the y-axis.

In the given equation:

m=2

Perpendicular lines have slopes that are negative reciprocals of each other.

First, we need to find its reciprocal.

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

Second, we need to rewrite it with the opposite sign.

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

Only one of the choices has a slope of $-\frac{1}{2}$ .

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

Report an Error

Example Question #16 : Perpendicular Lines

Find a line perpendicular to the line with the equation:

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

Possible Answers:

$y=-\frac{1}{5}x-8$

y=5x+2

y=-5x+5

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

Correct answer:

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

Explanation:

Lines can be written in the slope-intercept format:

y=mx+b

In this format, equals the line's slope and represents where the line intercepts the y-axis.

In the given equation:

m=-5

Perpendicular lines have slopes that are negative reciprocals of each other.

First, we need to find its reciprocal.

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

Second, we need to rewrite it with the opposite sign.

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

Only one of the choices has a slope of $\frac{1}{5}$ .

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

Report an Error

Example Question #17 : Perpendicular Lines

Find a line perpendicular to the line with the equation:

$y=\frac{3}{10}x-9$

Possible Answers:

$y=\frac{3}{10}x+100$

$y=-\frac{10}{3}x+98$

$y=\frac{10}{3}x+100$

$y=-\frac{3}{10}x-78$

Correct answer:

$y=-\frac{10}{3}x+98$

Explanation:

Lines can be written in the slope-intercept format:

y=mx+b

In this format, equals the line's slope and represents where the line intercepts the y-axis.

In the given equation:

$m=\frac{3}{10}$

Perpendicular lines have slopes that are negative reciprocals of each other.

First, we need to find its reciprocal.

$\frac{3}{10}\rightarrow\frac{10}{3}$

Second, we need to rewrite it with the opposite sign.

$\frac{10}{3}\rightarrow-\frac{10}{3}$

Only one of the choices has a slope of $-\frac{10}{3}$ .

$y=-\frac{10}{3}x+98$

Report an Error

Example Question #18 : Perpendicular Lines

Find a line perpendicular to the line with the equation:

y=100x-2

Possible Answers:

y=-102x-2

$y=-\frac{1}{100}x+85$

$y=\frac{1}{100}x+55$

y=100x+102

Correct answer:

$y=-\frac{1}{100}x+85$

Explanation:

Lines can be written in the slope-intercept format:

y=mx+b

In this format, equals the line's slope and represents where the line intercepts the y-axis.

In the given equation:

m=100

Perpendicular lines have slopes that are negative reciprocals of each other.

First, we need to find its reciprocal.

$100\rightarrow\frac{1}{100}$

Second, we need to rewrite it with the opposite sign.

$\frac{1}{100}\rightarrow-\frac{1}{100}$

Only one of the choices has a slope of $-\frac{1}{100}$ .

$y=-\frac{1}{100}x+85$

Report an Error

Example Question #19 : Perpendicular Lines

Given the two lines: y=2x and $y= -\frac{1}{2}x$ , are the lines perpendicular to each other?

Possible Answers:

$\textup{Yes, because both lines are in slope-intercept form.}$

$\textup{No, the slopes must be the same for both lines.}$

$\textup{Yes, the slopes are negative reciprocals of each other.}$

$\textup{No, because the slopes have no y-intercept.}$

$\textup{No, the slopes are not negative reciprocals of each other.}$

Correct answer:

$\textup{Yes, the slopes are negative reciprocals of each other.}$

Explanation:

Write the perpendicular line slope formula. The perpendicular slope is the negative reciprocal of the original slope.

$m_{perpendicular} = -\frac{1}{m_{original}}$

Let y=2x be the original equation. The slope is . Substitute this into the equation to find the slope of any perpendicular line.

$m_{perpendicular} = -\frac{1}{2}$

The slope of a perpendicular line must have a slope of $-\frac{1}{2}$ , which is also the slope for $y= -\frac{1}{2}x$ .

The answer is:

$\textup{Yes, the slopes are negative reciprocal to each other.}$

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Example Question #3541 : Algebra 1

Select the equation of the line that is perpendicular to $y=\frac{1}{2}x-4$ .

Possible Answers:

None of the other answers.

y=-2x+3

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

y=2x+3

y=2x-4

Correct answer:

y=-2x+3

Explanation:

Lines are perpendicular if their slopes are negative reciprocals of one another. For example, the negative reciprocal of $3=-\frac{1}{3}$ . So y=-2x+3 is perpendicular to $y=\frac{1}{2}x-4$ because their slopes are the negative reciprocals of each other. $\frac{1}{2}=-2\hspace{1mm}and\hspace{1mm} -2=-\frac{1}{-2}=\frac{1}{2}$ . A positive slope can still be the negative reciprocal as you can see.

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Algebra 1 : Equations of Lines

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #11 : Perpendicular Lines

Example Question #12 : Perpendicular Lines

Example Question #13 : Perpendicular Lines

Example Question #14 : Perpendicular Lines

Example Question #15 : Perpendicular Lines

Example Question #16 : Perpendicular Lines

Example Question #17 : Perpendicular Lines

Example Question #18 : Perpendicular Lines

Example Question #19 : Perpendicular Lines

Example Question #3541 : Algebra 1

All Algebra 1 Resources

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