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

$x - 7 y = 6$

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 $x$ from both sides of the equation.

$- 7 y = 6 - x$

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

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

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

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

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

Dividing two negative values results in a positive value.

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

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

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

$y = \frac{x}{7} - \frac{6}{7}$

Reorder terms.

$y = \frac{1}{7} x - \frac{6}{7}$

Step 2

Using the slope-intercept form, the slope is $\frac{1}{7}$ .

$m = \frac{1}{7}$

Step 3

The equation of a perpendicular line to $y = \frac{1}{7} x - \frac{6}{7}$ must have a slope that is the negative reciprocal of the original slope.

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

Step 4

Simplify the result.

Multiply the numerator by the reciprocal of the denominator.

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

Multiply $- (1 \cdot 7)$ .

Multiply $7$ by $1$ .

$m_{perpendicular} = - 1 \cdot 7$

Multiply $- 1$ by $7$ .

$m_{perpendicular} = - 7$

Step 5