Find the Slope of a Perpendicular Line 4x-5y=-3

$4 x - 5 y = - 3$

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 $4 x$ from both sides of the equation.

$- 5 y = - 3 - 4 x$

Divide each term in $- 5 y = - 3 - 4 x$ by $- 5$ and simplify.

Divide each term in $- 5 y = - 3 - 4 x$ by $- 5$ .

$\frac{- 5 y}{- 5} = \frac{- 3}{- 5} + \frac{- 4 x}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 y}{- 5} = \frac{- 3}{- 5} + \frac{- 4 x}{- 5}$

Divide $y$ by $1$ .

$y = \frac{- 3}{- 5} + \frac{- 4 x}{- 5}$

Simplify the right side.

Simplify each term.

Dividing two negative values results in a positive value.

$y = \frac{3}{5} + \frac{- 4 x}{- 5}$

Dividing two negative values results in a positive value.

$y = \frac{3}{5} + \frac{4 x}{5}$

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

Reorder $\frac{3}{5}$ and $\frac{4 x}{5}$ .

$y = \frac{4 x}{5} + \frac{3}{5}$

Reorder terms.

$y = \frac{4}{5} x + \frac{3}{5}$

Step 2

Using the slope-intercept form, the slope is $\frac{4}{5}$ .

$m = \frac{4}{5}$

Step 3

The equation of a perpendicular line to $y = \frac{4}{5} x + \frac{3}{5}$ must have a slope that is the negative reciprocal of the original slope.

$m_{perpendicular} = - \frac{1}{\frac{4}{5}}$

Step 4

Simplify the result.

Multiply the numerator by the reciprocal of the denominator.

$m_{perpendicular} = - (1 (\frac{5}{4}))$

Multiply $\frac{5}{4}$ by $1$ .

$m_{perpendicular} = - \frac{5}{4}$

Step 5