Find the Slope 5x-9y=45

$5 x - 9 y = 45$

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.

$- 9 y = 45 - 5 x$

Divide each term in $- 9 y = 45 - 5 x$ by $- 9$ and simplify.

Divide each term in $- 9 y = 45 - 5 x$ by $- 9$ .

$\frac{- 9 y}{- 9} = \frac{45}{- 9} + \frac{- 5 x}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 y}{- 9} = \frac{45}{- 9} + \frac{- 5 x}{- 9}$

Divide $y$ by $1$ .

$y = \frac{45}{- 9} + \frac{- 5 x}{- 9}$

Simplify the right side.

Simplify each term.

Divide $45$ by $- 9$ .

$y = - 5 + \frac{- 5 x}{- 9}$

Dividing two negative values results in a positive value.

$y = - 5 + \frac{5 x}{9}$

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

Reorder $- 5$ and $\frac{5 x}{9}$ .

$y = \frac{5 x}{9} - 5$

Reorder terms.

$y = \frac{5}{9} x - 5$

Step 2

Using the slope-intercept form, the slope is $\frac{5}{9}$ .

$m = \frac{5}{9}$

Step 3