Find the Slope and y-intercept -9x-3y=-6

$- 9 x - 3 y = - 6$

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.

$y = m x + b$

Add $9 x$ to both sides of the equation.

$- 3 y = - 6 + 9 x$

Divide each term in $- 3 y = - 6 + 9 x$ by $- 3$ and simplify.

Divide each term in $- 3 y = - 6 + 9 x$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{- 6}{- 3} + \frac{9 x}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{- 6}{- 3} + \frac{9 x}{- 3}$

Divide $y$ by $1$ .

$y = \frac{- 6}{- 3} + \frac{9 x}{- 3}$

Simplify the right side.

Simplify each term.

Divide $- 6$ by $- 3$ .

$y = 2 + \frac{9 x}{- 3}$

Cancel the common factor of $9$ and $- 3$ .

Factor $3$ out of $9 x$ .

$y = 2 + \frac{3 (3 x)}{- 3}$

Move the negative one from the denominator of $\frac{3 x}{- 1}$ .

$y = 2 - 1 \cdot (3 x)$

Rewrite $- 1 \cdot (3 x)$ as $- (3 x)$ .

$y = 2 - (3 x)$

Multiply $3$ by $- 1$ .

$y = 2 - 3 x$

Reorder $2$ and $- 3 x$ .

$y = - 3 x + 2$

Step 2

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

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

$m = - 3$

$b = 2$

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

Slope: $- 3$

y-intercept: $(0, 2)$

Slope: $- 3$

y-intercept: $(0, 2)$

Step 3