Find the Slope of a Perpendicular Line y=x+9

$y = x + 9$

Step 1

Use the slope-intercept form to find the slope.

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Using the slope-intercept form, the slope is $1$ .

$m = 1$

Step 2

The equation of a perpendicular line to $y = x + 9$ must have a slope that is the negative reciprocal of the original slope.

$m_{perpendicular} = - \frac{1}{1}$

Step 3

Simplify the result.

Cancel the common factor of $1$ .

Cancel the common factor.

$m_{perpendicular} = - \frac{1}{1}$

Rewrite the expression.

$m_{perpendicular} = - 1 \cdot 1$

Multiply $- 1$ by $1$ .

$m_{perpendicular} = - 1$

Step 4