Find the Slope of a Perpendicular Line y=1/5x+6

$y = \frac{1}{5} x + 6$

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.

$y = m x + b$

Simplify the right side.

Combine $\frac{1}{5}$ and $x$ .

$y = \frac{x}{5} + 6$

Reorder terms.

$y = \frac{1}{5} x + 6$

Step 2

Using the slope-intercept form, the slope is $\frac{1}{5}$ .

$m = \frac{1}{5}$

Step 3

The equation of a perpendicular line to $y = \frac{1}{5} x + 6$ must have a slope that is the negative reciprocal of the original slope.

$m_{perpendicular} = - \frac{1}{\frac{1}{5}}$

Step 4

Simplify the result.

Multiply the numerator by the reciprocal of the denominator.

$m_{perpendicular} = - (1 \cdot 5)$

Multiply $- (1 \cdot 5)$ .

Multiply $5$ by $1$ .

$m_{perpendicular} = - 1 \cdot 5$

Multiply $- 1$ by $5$ .

$m_{perpendicular} = - 5$

Step 5