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

$6 x + 3 y = - 3$

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 $6 x$ from both sides of the equation.

$3 y = - 3 - 6 x$

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

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

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Divide $- 3$ by $3$ .

$y = - 1 + \frac{- 6 x}{3}$

Cancel the common factor of $- 6$ and $3$ .

Factor $3$ out of $- 6 x$ .

$y = - 1 + \frac{3 (- 2 x)}{3}$

Cancel the common factors.

Factor $3$ out of $3$ .

$y = - 1 + \frac{3 (- 2 x)}{3 (1)}$

Cancel the common factor.

$y = - 1 + \frac{3 (- 2 x)}{3 \cdot 1}$

Rewrite the expression.

$y = - 1 + \frac{- 2 x}{1}$

Divide $- 2 x$ by $1$ .

$y = - 1 - 2 x$

Reorder $- 1$ and $- 2 x$ .

$y = - 2 x - 1$

Step 2

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

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

$m = - 2$

$b = - 1$

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

Slope: $- 2$

y-intercept: $(0, - 1)$

Slope: $- 2$

y-intercept: $(0, - 1)$

Step 3