Find the Slope of a Perpendicular Line y+x=5

$y + x = 5$

Step 1

Rewrite in slope-intercept form.

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

$y = m x + b$

Subtract $x$ from both sides of the equation.

$y = 5 - x$

Reorder $5$ and $- x$ .

$y = - x + 5$

Step 2

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

$m = - 1$

Step 3

The equation of a perpendicular line to $y = - x + 5$ must have a slope that is the negative reciprocal of the original slope.

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

Step 4

Simplify the result.

Divide $1$ by $- 1$ .

$m_{perpendicular} = 1$

Multiply $- 1$ by $- 1$ .

$m_{perpendicular} = 1$

Step 5