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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 #2 : How To Find The Slope Of Perpendicular Lines

What is the slope of a line that is perpendicular to

$y=\frac{6}{5}x-9$ ?

Possible Answers:

$\frac{6}{5}$

$-\frac{6}{5}$

$\frac{5}{6}$

$-\frac{5}{6}$

Correct answer:

$-\frac{5}{6}$

Explanation:

The slopes of perpendicular lines are negative inverses of each other. The slope of the given line is $\frac{6}{5}$ . The negative inverse of $\frac{6}{5}$ is $-\frac{5}{6}$ .

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Example Question #1 : How To Find The Slope Of Perpendicular Lines

Find the slope of a line that's perpendicular to the following linear equation:

y=-2x+9

Possible Answers:

none of these

$\frac{1}{2}$

$-\frac{1}{2}$

$\frac{1}{9}$

Correct answer:

$\frac{1}{2}$

Explanation:

We are given

y=-2x+9

To find the slope that's perpendicular, we perform the following steps

First, take the slope from our original equation. In our equation, the slope is
Take the reciprocal of that slope. The reciprocal is $-\frac{1}{2}$ .
Finally, change the sign so that we end up with $\frac{1}{2}$ . This is the number that represents the slope of the perpendicular line.

Another way to think of this problem is that the general formula for the slope that's perpendicular is

$slope_\perp=-\frac{1}{m}$

where is the slope of the original equation. In our case, m=-2 . Thus,

$slope_\perp=-\frac{1}{-2}=\frac{1}{2}$

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Example Question #2 : How To Find The Slope Of Perpendicular Lines

A line passes through points (–6,9) and (4,–4). Find the slope of the line that runs perpendicular to this line.

Possible Answers:

$-\frac{10}{13}$

$\frac{1}{3}$

$\frac{10}{13}$

$-\frac{13}{10}$

Correct answer:

$\frac{10}{13}$

Explanation:

To find the slope of this perpendicular line, we need to first find the slope of the line that passes through points (–6,9) and (4,–4). Remember, the general formula for slope is $m=\frac{y_2-y_1}{x_2-x_1}$ , where the two points are and . In our case, we can calculate the slope using out two points.

$m=\frac{-4-9}{4-(-6)}=-\frac{13}{10}$

The slope of the line passing through (–6,9) and (4,–4) is –13/10. To find the slope of the line that is perpendicular, just switch the sign and take the reciprocal of –13/10. This gives us 10/13. So 10/13 is the slope of that perpendicular line.

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Example Question #3 : How To Find The Slope Of Perpendicular Lines

Find the slope of the line perpendicular to the line that fits the following points:

(3,5), (2,7), (0,11)

Possible Answers:

$\frac{-2}{2}$

$\frac{1}{2}$

Correct answer:

$\frac{1}{2}$

Explanation:

1) To find the slope of the perpendicular line, we must first find the slope of the line fitting the given points. Slope is equal to change in over change in .

$\frac{7-5}{2-3}=\frac{2}{-1}=-2$

2) The perpendicular slope is the opposite reciprocal of the slope of the line to which it is perpendicular. So flip the original slope upside down and multiply by .

Perpendicular slope

$=\frac{1}{2}$

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

What is the slope of a line that is perpendicular to

$y=\frac{3}{2}x+9\ ?$

Possible Answers:

$-\frac{2}{3}$

None of the other answers

$\frac{2}{3}$

$-\frac{3}{2}$

$\frac{3}{2}$

Correct answer:

$-\frac{2}{3}$

Explanation:

Perpendicular lines have slopes that are negative reciprocals of one another. The slope of the given line is $\frac{3}{2}$ , which has a negative reciprocal of $-\frac{2}{3}$ .

Thus, the slope of the perpendicular line must be $-\frac{2}{3}$ .

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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:

$\frac{1}{2}$

$-\frac{1}{2}$

$\frac{1}{5}$

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 #16 : 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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Algebra 1 : Functions and Lines

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #2 : How To Find The Slope Of Perpendicular Lines

Example Question #1 : How To Find The Slope Of Perpendicular Lines

Example Question #2 : How To Find The Slope Of Perpendicular Lines

Example Question #3 : How To Find The Slope Of Perpendicular Lines

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

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 #16 : How To Find The Slope Of Perpendicular Lines

All Algebra 1 Resources

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