Find the Slope 5x-3y=4

$5 x - 3 y = 4$

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.

$- 3 y = 4 - 5 x$

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

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

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

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

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

Dividing two negative values results in a positive value.

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

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

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

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

Reorder terms.

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

Step 2

Using the slope-intercept form, the slope is $\frac{5}{3}$ .

$m = \frac{5}{3}$

Step 3