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Algebra 1 : Equations of Lines

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #11 : How To Find The Slope Of Perpendicular Lines

What is the slope of a line which is perpendicular to the following line?

$y=\frac{5}{9}x+8$

Possible Answers:

$\frac{5}{9}$

$\frac{9}{5}$

$-\frac{9}{5}$

Correct answer:

$-\frac{9}{5}$

Explanation:

Given that our equation is in slop-intercept form

y=mx+b

$y=\frac{5}{9}x+8$

where is the slope, we see that for this line the slope is $\frac{5}{9}$ .

Find the negative reciprocal of the slope to find the perpendicular line's slope.

Flip the fraction and make it negative.

$\frac{5}{9}\rightarrow -\frac{9}{5}$ .

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Example Question #11 : How To Find The Slope Of Perpendicular Lines

What is the slope of a line perpendicular to $y=-\frac{1}{2}x-5$ ?

Possible Answers:

$\frac{1}{2}$

$\frac{1}{5}$

$-\frac{1}{2}$

Correct answer:

Explanation:

Perpendicular lines are lines that intersect each other at a ninety degree angle. The slope of a line that is perpendicular to another has the opposite sign and is the reciprocal. The slope of a line perpendicular to the one given would be .

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Example Question #43 : Perpendicular Lines

$\\ \textup{The slope of a side of a square is 3.}\\\textup{Which of these values cannot be the slope of one of the other three sides?}$

Possible Answers:

$\frac{1}{3}$

$\textup{None of the above.}$

$\textup{All of the above.}$

$-\frac{1}{3}$

Correct answer:

$\frac{1}{3}$

Explanation:

$\textup{Of the other three sides, the opposite side lays on a parallel line,}\\\textup{ so its slope is 3 as well. The two adjacent sides lay on perpendicular lines,}\\\textup{ so their slope is the inverse reciprocal of 3; that is, } -\frac{1}{3}.$

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Example Question #11 : How To Find The Slope Of Perpendicular Lines

$\\\textup{Two opposite vertices of a square are the points (0,0) and (-2,4).}\\\textup{Which can be one of the other two vertices?}$

Possible Answers:

(1,3)

(1,2)

(-2,-1)

(1,4)

(-2,0)

Correct answer:

(1,3)

Explanation:

$\textup{The segment between the two opposite vertices (0,0) and (-2,4) is one }\\\textup{diagonal of the square with slope}\frac{4}{-2}=-2 \textup{ and midpoint } \left(\frac{0+(-2)}{2},\frac{0+4}{2} \right)=(-1,2). \textup{ The other diagonal lays on the line } y=\frac{1}{2}x+p \textup{ since it is perpendicular}\\\textup{ and has as a slope of the inverse reciprocal. Substituting the midpoint into the }\\\textup{ parametric equation we obtain } p=\frac{5}{2}\textup{ and the line equation } y=\frac{1}{2}c+\frac{5}{2}.$

$\textup{ Only point } (1,3) \textup{ among the possible answers lays on this line.}$ .

$\textup{ Alternatively, one can check for every possible answer if the two segments}\\\textup{between the candidate point and the two opposite vertices are perpendicular.}$

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Example Question #12 : How To Find The Slope Of Perpendicular Lines

Find the slope of the line perpendicular to y=3x+4 .

Possible Answers:

1/3

-1/3

Correct answer:

-1/3

Explanation:

The slope of a perpendicular line is always the negative reciprocal of the original slope.

Our original equation is y=3x+4 which is in the form y=mx+b where is the slope. Therefore, the original slope is m=3 .

To find the slope of a line perpendicular we want to use the following formula,

$m_p=-\frac{1}{m}$

$m_p=-\frac{1}{3}$ .

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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.

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

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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:

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

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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Algebra 1 : Equations of Lines

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #11 : How To Find The Slope Of Perpendicular Lines

Example Question #11 : How To Find The Slope Of Perpendicular Lines

Example Question #43 : Perpendicular Lines

Example Question #11 : How To Find The Slope Of Perpendicular Lines

Example Question #12 : How To Find The Slope Of Perpendicular Lines

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

All Algebra 1 Resources

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