Find the Slope and y-intercept 4x+9y-36=0

$4 x + 9 y - 36 = 0$

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.

$y = m x + b$

Move all terms not containing $y$ to the right side of the equation.

Subtract $4 x$ from both sides of the equation.

$9 y - 36 = - 4 x$

Add $36$ to both sides of the equation.

$9 y = - 4 x + 36$

Divide each term in $9 y = - 4 x + 36$ by $9$ and simplify.

Divide each term in $9 y = - 4 x + 36$ by $9$ .

$\frac{9 y}{9} = \frac{- 4 x}{9} + \frac{36}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 y}{9} = \frac{- 4 x}{9} + \frac{36}{9}$

Divide $y$ by $1$ .

$y = \frac{- 4 x}{9} + \frac{36}{9}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{(4) x}{9} + \frac{36}{9}$

Divide $36$ by $9$ .

$y = - \frac{4 x}{9} + 4$

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

Reorder terms.

$y = - (\frac{4}{9} x) + 4$

Remove parentheses.

$y = - \frac{4}{9} x + 4$

Step 2

Use the slope-intercept form to find the slope and y-intercept.

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = - \frac{4}{9}$

$b = 4$

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $- \frac{4}{9}$

y-intercept: $(0, 4)$

Slope: $- \frac{4}{9}$

y-intercept: $(0, 4)$

Step 3