Find the Slope 5x-4y=8

$5 x - 4 y = 8$

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 $5 x$ from both sides of the equation.

$- 4 y = 8 - 5 x$

Divide each term in $- 4 y = 8 - 5 x$ by $- 4$ and simplify.

Divide each term in $- 4 y = 8 - 5 x$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{8}{- 4} + \frac{- 5 x}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{8}{- 4} + \frac{- 5 x}{- 4}$

Divide $y$ by $1$ .

$y = \frac{8}{- 4} + \frac{- 5 x}{- 4}$

Simplify the right side.

Simplify each term.

Divide $8$ by $- 4$ .

$y = - 2 + \frac{- 5 x}{- 4}$

Dividing two negative values results in a positive value.

$y = - 2 + \frac{5 x}{4}$

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

Reorder $- 2$ and $\frac{5 x}{4}$ .

$y = \frac{5 x}{4} - 2$

Reorder terms.

$y = \frac{5}{4} x - 2$

Step 2

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

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

Step 3