Find the Slope of a Perpendicular Line 2x-y=16

$2 x - y = 16$

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 $2 x$ from both sides of the equation.

$- y = 16 - 2 x$

Divide each term in $- y = 16 - 2 x$ by $- 1$ and simplify.

Divide each term in $- y = 16 - 2 x$ by $- 1$ .

$\frac{- y}{- 1} = \frac{16}{- 1} + \frac{- 2 x}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{16}{- 1} + \frac{- 2 x}{- 1}$

Divide $y$ by $1$ .

$y = \frac{16}{- 1} + \frac{- 2 x}{- 1}$

Simplify the right side.

Simplify each term.

Divide $16$ by $- 1$ .

$y = - 16 + \frac{- 2 x}{- 1}$

Move the negative one from the denominator of $\frac{- 2 x}{- 1}$ .

$y = - 16 - 1 \cdot (- 2 x)$

Rewrite $- 1 \cdot (- 2 x)$ as $- (- 2 x)$ .

$y = - 16 - (- 2 x)$

Multiply $- 2$ by $- 1$ .

$y = - 16 + 2 x$

Reorder $- 16$ and $2 x$ .

$y = 2 x - 16$

Step 2

Using the slope-intercept form, the slope is $2$ .

$m = 2$

Step 3

The equation of a perpendicular line to $y = 2 x - 16$ must have a slope that is the negative reciprocal of the original slope.

$m_{perpendicular} = - \frac{1}{2}$

Step 4