ACT Math : How to find the slope of a perpendicular line

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #21 : Perpendicular Lines

Give the slope of the line perpendicular to .

Possible Answers:

Correct answer:

Explanation:

To find the slope of a perpendicular line, we take the reciprocal  of the known slope , where 

The easy way to do this is to simply take the fraction (a whole slope can be made into a fraction by placing  in the denominator), exchange the numerator and denominator, then multiply the fraction by  Thus,

.

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

Calculate the slope of a line perpendicular to the line with the following equation:

Possible Answers:

None of these

Correct answer:

Explanation:

Perpendicular lines will have slopes that are negative reciprocals of one another. Our first step will be to find the slope of the given line by putting the equation into slope-intercept form.

The slope of this line is .

 

First let's find the negative of the current slope.

Now, we need to find the reciprocal of . In order to find the reciprocal of a number we divide one by that number; therefore, we can calculate the following:

The negative reciprocal will be   or  which will be the slope of the perpendicular line.

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