Find the Slope of a Parallel Line 4x-5y=7

$4 x - 5 y = 7$

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.

$- 5 y = 7 - 4 x$

Divide each term in $- 5 y = 7 - 4 x$ by $- 5$ and simplify.

Divide each term in $- 5 y = 7 - 4 x$ by $- 5$ .

$\frac{- 5 y}{- 5} = \frac{7}{- 5} + \frac{- 4 x}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 y}{- 5} = \frac{7}{- 5} + \frac{- 4 x}{- 5}$

Divide $y$ by $1$ .

$y = \frac{7}{- 5} + \frac{- 4 x}{- 5}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{7}{5} + \frac{- 4 x}{- 5}$

Dividing two negative values results in a positive value.

$y = - \frac{7}{5} + \frac{4 x}{5}$

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

Reorder $- \frac{7}{5}$ and $\frac{4 x}{5}$ .

$y = \frac{4 x}{5} - \frac{7}{5}$

Reorder terms.

$y = \frac{4}{5} x - \frac{7}{5}$

Step 2

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

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

Step 3

All lines that are parallel to $y = \frac{4}{5} x - \frac{7}{5}$ have the same slope of $\frac{4}{5}$ .

$m_{parallel} = \frac{4}{5}$

Step 4