### All High School Math Resources

## Example Questions

### Example Question #8 : Perpendicular Lines

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:**

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 #9 : Perpendicular Lines

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

**Possible Answers:**

**Correct answer:**

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

What will be the slope of the line perpendicular to ?

**Possible Answers:**

**Correct answer:**

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 #11 : Perpendicular Lines

Which of the following is perpendicular to the line described by

**Possible Answers:**

**Correct answer:**

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 #12 : Perpendicular Lines

Which of the following is perpendicular to the line described by

**Possible Answers:**

**Correct answer:**

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 #2 : 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:**

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 #41 : Lines

Find the slope of the line perpendicular to .

**Possible Answers:**

**Correct answer:**

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

What is the slope of the line perpendicular to ?

**Possible Answers:**

**Correct answer:**

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

Find the slope of this line:

**Possible Answers:**

**Correct answer:**

Isolate for so that the equation now reads

The slope is .

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