Find the Slope of a Perpendicular Line 3x-7y=-2

$3 x - 7 y = - 2$

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.

$y = m x + b$

Subtract $3 x$ from both sides of the equation.

$- 7 y = - 2 - 3 x$

Divide each term in $- 7 y = - 2 - 3 x$ by $- 7$ and simplify.

Divide each term in $- 7 y = - 2 - 3 x$ by $- 7$ .

$\frac{- 7 y}{- 7} = \frac{- 2}{- 7} + \frac{- 3 x}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 y}{- 7} = \frac{- 2}{- 7} + \frac{- 3 x}{- 7}$

Divide $y$ by $1$ .

$y = \frac{- 2}{- 7} + \frac{- 3 x}{- 7}$

Simplify the right side.

Simplify each term.

Dividing two negative values results in a positive value.

$y = \frac{2}{7} + \frac{- 3 x}{- 7}$

Dividing two negative values results in a positive value.

$y = \frac{2}{7} + \frac{3 x}{7}$

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

Reorder $\frac{2}{7}$ and $\frac{3 x}{7}$ .

$y = \frac{3 x}{7} + \frac{2}{7}$

Reorder terms.

$y = \frac{3}{7} x + \frac{2}{7}$

Step 2

Using the slope-intercept form, the slope is $\frac{3}{7}$ .

$m = \frac{3}{7}$

Step 3

The equation of a perpendicular line to $y = \frac{3}{7} x + \frac{2}{7}$ must have a slope that is the negative reciprocal of the original slope.

$m_{perpendicular} = - \frac{1}{\frac{3}{7}}$

Step 4

Simplify the result.

Multiply the numerator by the reciprocal of the denominator.

$m_{perpendicular} = - (1 (\frac{7}{3}))$

Multiply $\frac{7}{3}$ by $1$ .

$m_{perpendicular} = - \frac{7}{3}$

Step 5