Algebra - How to find the slope of perpendicular lines

Find the slope of the line perpendicular to

$-\frac{1}{3}$

$\frac{1}{3}$

$-\frac{1}{5}$

$\frac{1}{5}$

Explanation

A line perpendicular to another line has a slope that is the negative reciprocal of the other. In our case, the line given has a slope of ( in the form ), so the line perpendicular to it must have a slope equal to $-\frac{1}{3}$ .

What's the slope of the line perpendicular to ?

$-\frac{1}{2}$

$-\frac{1}{5}$

Explanation

When finding the slope of a perpendicular line, we need to ensure we have form.

stands for slope.

Our is .

To find the perpendicular slope, we need to take the negative reciprocal of that value which is $-\frac{1}{2}$ .

Find the slope of the line that is perpendicular to a line with the equation:

$-\frac{1}{2}$

$\frac{1}{2}$

Explanation

Lines can be written in the slope-intercept form:

In this equation, is the slope and is the y-intercept.

Lines that are perpendicular to each other have slopes that are negative reciprocals of each other. This means that you need to flip the numerator and denominator of the given slope and then change the sign.

First, find the reciprocal of :

$2=\frac{2}{1}$

Flip the numerator and the denominator.

$\frac{2}{1}\rightarrow \frac{1}{2}$

Next, change the sign.

$\frac{1}{2}\rightarrow-\frac{1}{2}$

What is the slope of the line perpendicular to the equation ?

$\frac{4}{5}$

$-\frac{5}{4}$

$\frac{1}{5}$

Explanation

When finding the slope of a perpendicular line, we need to ensure we have form.

We need to solve for .

By subtracting both sides and dividing on both sides, we get

$y=\frac{7-5x}{4}$

Recall that stands for slope.

Our is $-\frac{5}{4}$ .

To find the perpendicular slope, we need to take the negative reciprocal of that value which is $\frac{4}{5}$ .

Find the slope of the line that is perpendicular to the line that contains (1, 9) and (3, 4).

2/5

–2/5

–5/2

5/2

4/3

Explanation

The slope of the line that contains the points (1, 9) and (3, 4) is $\frac{4-9}{3-1}=\frac{-5}{2}$ .

$slope=\frac{y_2-y_1}{x_2-x_1}=\frac{4-9}{3-1}=-\frac{5}{2}$

The negative reciprocal is $\frac{2}{5}$ , which is the slope of the perpendicular line.

Find the slope of the line that is perpendicular to a line with the equation:

$y=\frac{1}{3}x-9$

$-\frac{1}{3}$

$\frac{1}{3}$

Explanation

Lines can be written in the slope-intercept form:

In this equation, is the slope and is the y-intercept.

First, find the reciprocal of $\frac{1}{3}$ .

$\frac{1}{3}\rightarrow \frac{3}{1}=3$

Next, change the sign.

$3\rightarrow-3$

What is the slope of a line that is perpendicular to

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

$-\frac{5}{6}$

$\frac{5}{6}$

$\frac{6}{5}$

$-\frac{6}{5}$

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 $-\frac{5}{6}$ .