Find the Slope of a Perpendicular Line 4x-2y=1

$4 x - 2 y = 1$

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 $4 x$ from both sides of the equation.

$- 2 y = 1 - 4 x$

Divide each term in $- 2 y = 1 - 4 x$ by $- 2$ and simplify.

Divide each term in $- 2 y = 1 - 4 x$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{1}{- 2} + \frac{- 4 x}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{1}{- 2} + \frac{- 4 x}{- 2}$

Divide $y$ by $1$ .

$y = \frac{1}{- 2} + \frac{- 4 x}{- 2}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{1}{2} + \frac{- 4 x}{- 2}$

Cancel the common factor of $- 4$ and $- 2$ .

Factor $- 2$ out of $- 4 x$ .

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

Cancel the common factors.

Factor $- 2$ out of $- 2$ .

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

Cancel the common factor.

$y = - \frac{1}{2} + \frac{- 2 (2 x)}{- 2 \cdot 1}$

Rewrite the expression.

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

Divide $2 x$ by $1$ .

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

Reorder $- \frac{1}{2}$ and $2 x$ .

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

Step 2

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

$m = 2$

Step 3

The equation of a perpendicular line to $y = 2 x - \frac{1}{2}$ must have a slope that is the negative reciprocal of the original slope.

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

Step 4