Find the Slope 5x-6y=30

$5 x - 6 y = 30$

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.

$- 6 y = 30 - 5 x$

Divide each term in $- 6 y = 30 - 5 x$ by $- 6$ and simplify.

Divide each term in $- 6 y = 30 - 5 x$ by $- 6$ .

$\frac{- 6 y}{- 6} = \frac{30}{- 6} + \frac{- 5 x}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 y}{- 6} = \frac{30}{- 6} + \frac{- 5 x}{- 6}$

Divide $y$ by $1$ .

$y = \frac{30}{- 6} + \frac{- 5 x}{- 6}$

Simplify the right side.

Simplify each term.

Divide $30$ by $- 6$ .

$y = - 5 + \frac{- 5 x}{- 6}$

Dividing two negative values results in a positive value.

$y = - 5 + \frac{5 x}{6}$

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

Reorder $- 5$ and $\frac{5 x}{6}$ .

$y = \frac{5 x}{6} - 5$

Reorder terms.

$y = \frac{5}{6} x - 5$

Step 2

Using the slope-intercept form, the slope is $\frac{5}{6}$ .

$m = \frac{5}{6}$

Step 3