Find the Slope of a Perpendicular Line 12x-13y=1

$12 x - 13 y = 1$

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 $12 x$ from both sides of the equation.

$- 13 y = 1 - 12 x$

Divide each term in $- 13 y = 1 - 12 x$ by $- 13$ and simplify.

Divide each term in $- 13 y = 1 - 12 x$ by $- 13$ .

$\frac{- 13 y}{- 13} = \frac{1}{- 13} + \frac{- 12 x}{- 13}$

Simplify the left side.

Cancel the common factor of $- 13$ .

Cancel the common factor.

$\frac{- 13 y}{- 13} = \frac{1}{- 13} + \frac{- 12 x}{- 13}$

Divide $y$ by $1$ .

$y = \frac{1}{- 13} + \frac{- 12 x}{- 13}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{1}{13} + \frac{- 12 x}{- 13}$

Dividing two negative values results in a positive value.

$y = - \frac{1}{13} + \frac{12 x}{13}$

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

Reorder $- \frac{1}{13}$ and $\frac{12 x}{13}$ .

$y = \frac{12 x}{13} - \frac{1}{13}$

Reorder terms.

$y = \frac{12}{13} x - \frac{1}{13}$

Step 2

Using the slope-intercept form, the slope is $\frac{12}{13}$ .

$m = \frac{12}{13}$

Step 3

The equation of a perpendicular line to $y = \frac{12}{13} x - \frac{1}{13}$ must have a slope that is the negative reciprocal of the original slope.

$m_{perpendicular} = - \frac{1}{\frac{12}{13}}$

Step 4

Simplify the result.

Multiply the numerator by the reciprocal of the denominator.

$m_{perpendicular} = - (1 (\frac{13}{12}))$

Multiply $\frac{13}{12}$ by $1$ .

$m_{perpendicular} = - \frac{13}{12}$

Step 5