Find the Slope and y-intercept 4y-8x+12=0

$4 y - 8 x + 12 = 0$

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.

Add $8 x$ to both sides of the equation.

$4 y + 12 = 8 x$

Subtract $12$ from both sides of the equation.

$4 y = 8 x - 12$

Divide each term in $4 y = 8 x - 12$ by $4$ and simplify.

Divide each term in $4 y = 8 x - 12$ by $4$ .

$\frac{4 y}{4} = \frac{8 x}{4} + \frac{- 12}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} = \frac{8 x}{4} + \frac{- 12}{4}$

Divide $y$ by $1$ .

$y = \frac{8 x}{4} + \frac{- 12}{4}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $8$ and $4$ .

Factor $4$ out of $8 x$ .

$y = \frac{4 (2 x)}{4} + \frac{- 12}{4}$

Cancel the common factors.

Factor $4$ out of $4$ .

$y = \frac{4 (2 x)}{4 (1)} + \frac{- 12}{4}$

Cancel the common factor.

$y = \frac{4 (2 x)}{4 \cdot 1} + \frac{- 12}{4}$

Rewrite the expression.

$y = \frac{2 x}{1} + \frac{- 12}{4}$

Divide $2 x$ by $1$ .

$y = 2 x + \frac{- 12}{4}$

Divide $- 12$ by $4$ .

$y = 2 x - 3$

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

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

$m = 2$

$b = - 3$

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

Slope: $2$

y-intercept: $(0, - 3)$

Slope: $2$

y-intercept: $(0, - 3)$