How to find the slope of a perpendicular line - Math

Card 0 of 36

Question

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

Answer

The original line has a slope of $\frac{11}{3}$ , a line perpendicular to the original line will have a slope which is the negative reciprocal of this value.

Compare your answer with the correct one above

Question

Find the slope of the line perpendicular to $y + \frac{2}{3}x = 12$ .

Answer

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

Do this by subtracting $\frac{2}{3}x$ from both sides of the equation:

$y = -\frac{2}{3}x + 12$

The slope of this line is $-\frac{2}{3}$ .

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

$-\frac{2}{3} \Rightarrow -\frac{3}{2} \Rightarrow -\frac{3}{2} \times -1 \Rightarrow \frac{3}{2}$

Compare your answer with the correct one above

Question

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

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

Thus, we can determine that $y = -\frac{1}{3}x + 10$ is the only choice with the correct slope.

Compare your answer with the correct one above

Question

Find the slope of this line:

Answer

Isolate for so that the equation now reads

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

The slope is $\frac{1}{4}$ .

Compare your answer with the correct one above

Question

Which of the following is perpendicular to the line described by

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

The answer

$y=-\frac{1}{3}x+2$

is the only equation listed that has a slope of $-\frac{1}{3}$ .

Compare your answer with the correct one above

Question

Which of the following is perpendicular to the line described by

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 $\frac{1}{6}$ .

The answer

$y = \frac{1}{6}x+9$

is the only equation listed that has a slope of $\frac{1}{6}$ .

Compare your answer with the correct one above

Question

What will be the slope of the line perpendicular to $y=3x+\frac{1}{2}$ ?

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

Compare your answer with the correct one above

Question

What is the slope of the line perpendicular to $y=\frac{2}{3}x+\frac{1}{2}$ ?

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 $\frac{2}{3}$ . Therefore, the slope of the perpendicular line is $-\frac{3}{2}$ .

Compare your answer with the correct one above

Question

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

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 $\frac{1}{3}$ .

Compare your answer with the correct one above

Question

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

Answer

The original line has a slope of $\frac{11}{3}$ , a line perpendicular to the original line will have a slope which is the negative reciprocal of this value.

Compare your answer with the correct one above

Question

Find the slope of the line perpendicular to $y + \frac{2}{3}x = 12$ .

Answer

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

Do this by subtracting $\frac{2}{3}x$ from both sides of the equation:

$y = -\frac{2}{3}x + 12$

The slope of this line is $-\frac{2}{3}$ .

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

$-\frac{2}{3} \Rightarrow -\frac{3}{2} \Rightarrow -\frac{3}{2} \times -1 \Rightarrow \frac{3}{2}$

Compare your answer with the correct one above

Question

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

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

Thus, we can determine that $y = -\frac{1}{3}x + 10$ is the only choice with the correct slope.

Compare your answer with the correct one above

Question

Find the slope of this line:

Answer

Isolate for so that the equation now reads

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

The slope is $\frac{1}{4}$ .

Compare your answer with the correct one above

Question

Which of the following is perpendicular to the line described by

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

The answer

$y=-\frac{1}{3}x+2$

is the only equation listed that has a slope of $-\frac{1}{3}$ .

Compare your answer with the correct one above

Question

Which of the following is perpendicular to the line described by

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 $\frac{1}{6}$ .

The answer

$y = \frac{1}{6}x+9$

is the only equation listed that has a slope of $\frac{1}{6}$ .

Compare your answer with the correct one above

Question

What will be the slope of the line perpendicular to $y=3x+\frac{1}{2}$ ?

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

Compare your answer with the correct one above

Question

What is the slope of the line perpendicular to $y=\frac{2}{3}x+\frac{1}{2}$ ?

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 $\frac{2}{3}$ . Therefore, the slope of the perpendicular line is $-\frac{3}{2}$ .

Compare your answer with the correct one above

Question

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

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 $\frac{1}{3}$ .

Compare your answer with the correct one above

Question

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

Answer

The original line has a slope of $\frac{11}{3}$ , a line perpendicular to the original line will have a slope which is the negative reciprocal of this value.

Compare your answer with the correct one above

Question

Find the slope of the line perpendicular to $y + \frac{2}{3}x = 12$ .

Answer

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

Do this by subtracting $\frac{2}{3}x$ from both sides of the equation:

$y = -\frac{2}{3}x + 12$

The slope of this line is $-\frac{2}{3}$ .

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

$-\frac{2}{3} \Rightarrow -\frac{3}{2} \Rightarrow -\frac{3}{2} \times -1 \Rightarrow \frac{3}{2}$

Compare your answer with the correct one above

Tap the card to reveal the answer