Write in Slope-Intercept Form y-7=-1/3(x+9)

$y - 7 = - \frac{1}{3} (x + 9)$

Step 1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 2

Rewrite in slope-intercept form.

Simplify the right side.

Simplify $- \frac{1}{3} (x + 9)$ .

Apply the distributive property.

$y - 7 = - \frac{1}{3} x - \frac{1}{3} \cdot 9$

Combine $x$ and $\frac{1}{3}$ .

$y - 7 = - \frac{x}{3} - \frac{1}{3} \cdot 9$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$y - 7 = - \frac{x}{3} + \frac{- 1}{3} \cdot 9$

Factor $3$ out of $9$ .

$y - 7 = - \frac{x}{3} + \frac{- 1}{3} \cdot (3 (3))$

Cancel the common factor.

$y - 7 = - \frac{x}{3} + \frac{- 1}{3} \cdot (3 \cdot 3)$

Rewrite the expression.

$y - 7 = - \frac{x}{3} - 1 \cdot 3$

Multiply $- 1$ by $3$ .

$y - 7 = - \frac{x}{3} - 3$

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

Add $7$ to both sides of the equation.

$y = - \frac{x}{3} - 3 + 7$

Add $- 3$ and $7$ .

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

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

Reorder terms.

$y = - (\frac{1}{3} x) + 4$

Remove parentheses.

$y = - \frac{1}{3} x + 4$