Find the Slope of a Perpendicular Line -7x+2y=-2

$- 7 x + 2 y = - 2$

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.

$y = m x + b$

Add $7 x$ to both sides of the equation.

$2 y = - 2 + 7 x$

Divide each term in $2 y = - 2 + 7 x$ by $2$ and simplify.

Divide each term in $2 y = - 2 + 7 x$ by $2$ .

$\frac{2 y}{2} = \frac{- 2}{2} + \frac{7 x}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{- 2}{2} + \frac{7 x}{2}$

Divide $y$ by $1$ .

$y = \frac{- 2}{2} + \frac{7 x}{2}$

Simplify the right side.

Divide $- 2$ by $2$ .

$y = - 1 + \frac{7 x}{2}$

Write in $y = m x + b$ form.

Reorder $- 1$ and $\frac{7 x}{2}$ .

$y = \frac{7 x}{2} - 1$

Reorder terms.

$y = \frac{7}{2} x - 1$

Step 2

Using the slope-intercept form, the slope is $\frac{7}{2}$ .

$m = \frac{7}{2}$

Step 3

The equation of a perpendicular line to $y = \frac{7}{2} x - 1$ must have a slope that is the negative reciprocal of the original slope.

$m_{perpendicular} = - \frac{1}{\frac{7}{2}}$

Step 4

Simplify the result.

Multiply the numerator by the reciprocal of the denominator.

$m_{perpendicular} = - (1 (\frac{2}{7}))$

Multiply $\frac{2}{7}$ by $1$ .

$m_{perpendicular} = - \frac{2}{7}$

Step 5