Find the Slope and y-intercept 12x+3y=9

$12 x + 3 y = 9$

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 $12 x$ from both sides of the equation.

$3 y = 9 - 12 x$

Divide each term in $3 y = 9 - 12 x$ by $3$ and simplify.

Divide each term in $3 y = 9 - 12 x$ by $3$ .

$\frac{3 y}{3} = \frac{9}{3} + \frac{- 12 x}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{9}{3} + \frac{- 12 x}{3}$

Divide $y$ by $1$ .

$y = \frac{9}{3} + \frac{- 12 x}{3}$

Simplify the right side.

Simplify each term.

Divide $9$ by $3$ .

$y = 3 + \frac{- 12 x}{3}$

Cancel the common factor of $- 12$ and $3$ .

Factor $3$ out of $- 12 x$ .

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

Cancel the common factors.

Factor $3$ out of $3$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $- 4 x$ by $1$ .

$y = 3 - 4 x$

Reorder $3$ and $- 4 x$ .

$y = - 4 x + 3$

Step 2

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

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

$m = - 4$

$b = 3$

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

Slope: $- 4$

y-intercept: $(0, 3)$

Slope: $- 4$

y-intercept: $(0, 3)$

Step 3