High School Math : How to find the slope of a perpendicular line

Study concepts, example questions & explanations for High School Math

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Example Questions

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

A line passes through the points  and .  If a new line is drawn perpendicular to the original line, what will its slope be?

Possible Answers:

Correct answer:

Explanation:

The original line has a slope of , a line perpendicular to the original line will have a slope which is the negative reciprocal of this value.

Example Question #7 : Perpendicular Lines

Which of the following is the equation of a line that is perpendicular to the line  ? 

Possible Answers:

Correct answer:

Explanation:

Perpendicular lines have slopes that are the opposite reciprocals of each other. Thus, we first identify the slope of the given line, which is  (since it is in the form , where  represents slope).

Then, we know that any line which is perpendicular to this will have a slope of .

Thus, we can determine that  is the only choice with the correct slope. 

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

What will be the slope of the line perpendicular to ?

Possible Answers:

Correct answer:

Explanation:

In standard form, the is the slope.

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

For our given line, the slope is . Therefore, the slope of the perpendicular line is .

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

Which of the following is perpendicular to the line described by

Possible Answers:

Correct answer:

Explanation:

The definition of perpendicular lines is that their slopes are inverse reciprocals of one another. Since the slope in the given equation is , this means that the slope of its perpendicular line would be .

 

The answer 

 

is the only equation listed that has a slope of .

Example Question #4 : How To Find The Slope Of A Perpendicular Line

Which of the following is perpendicular to the line described by 

Possible Answers:

Correct answer:

Explanation:

The definition of perpendicular lines is that their slopes are inverse reciprocals of one another. Since the slope in the given equation is , this means that the slope of its perpendicular line would be .

 

The answer 

 

is the only equation listed that has a slope of .

Example Question #5 : How To Find The Slope Of A Perpendicular Line

Which of the following gives the slope of a line that is perpendicular to  ? 

Possible Answers:

Correct answer:

Explanation:

Recall that the slopes of perpendicular lines are opposite reciprocals of one another. As a result, we are looking for the opposite reciprocal of . Thus, we can get that the opposite reciprocal is 

Example Question #6 : How To Find The Slope Of A Perpendicular Line

Find the slope of the line perpendicular to .

Possible Answers:

Correct answer:

Explanation:

Put this equation into slope-intercept form, y = mx + b, to find the slope, m.

Do this by subtracting  from both sides of the equation:

The slope of this line is .

The slope of the perpendicular line is the negative reciprocal. Switch the numerator and denominator, and then multiply by :

Example Question #6 : How To Find The Slope Of A Perpendicular Line

What is the slope of the line perpendicular to ?

Possible Answers:

Correct answer:

Explanation:

In standard form, is the slope.

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

For our given line, the slope is . Therefore, the slope of the perpendicular line is .

 

Example Question #7 : How To Find The Slope Of A Perpendicular Line

Find the slope of this line: 

Possible Answers:

Correct answer:

Explanation:

Isolate for  so that the equation now reads 

The slope is 

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