Find the Slope of a Perpendicular Line -6x+7y=2

$- 6 x + 7 y = 2$

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.

$y = m x + b$

Add $6 x$ to both sides of the equation.

$7 y = 2 + 6 x$

Divide each term in $7 y = 2 + 6 x$ by $7$ and simplify.

Divide each term in $7 y = 2 + 6 x$ by $7$ .

$\frac{7 y}{7} = \frac{2}{7} + \frac{6 x}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 y}{7} = \frac{2}{7} + \frac{6 x}{7}$

Divide $y$ by $1$ .

$y = \frac{2}{7} + \frac{6 x}{7}$

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

Reorder $\frac{2}{7}$ and $\frac{6 x}{7}$ .

$y = \frac{6 x}{7} + \frac{2}{7}$

Reorder terms.

$y = \frac{6}{7} x + \frac{2}{7}$

Step 2

Using the slope-intercept form, the slope is $\frac{6}{7}$ .

$m = \frac{6}{7}$

Step 3

The equation of a perpendicular line to $y = \frac{6}{7} x + \frac{2}{7}$ must have a slope that is the negative reciprocal of the original slope.

$m_{perpendicular} = - \frac{1}{\frac{6}{7}}$

Step 4

Simplify the result.

Multiply the numerator by the reciprocal of the denominator.

$m_{perpendicular} = - (1 (\frac{7}{6}))$

Multiply $\frac{7}{6}$ by $1$ .

$m_{perpendicular} = - \frac{7}{6}$

Step 5