Find the Slope and y-intercept 2x-6y=12

$2 x - 6 y = 12$

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 $2 x$ from both sides of the equation.

$- 6 y = 12 - 2 x$

Divide each term in $- 6 y = 12 - 2 x$ by $- 6$ and simplify.

Divide each term in $- 6 y = 12 - 2 x$ by $- 6$ .

$\frac{- 6 y}{- 6} = \frac{12}{- 6} + \frac{- 2 x}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 y}{- 6} = \frac{12}{- 6} + \frac{- 2 x}{- 6}$

Divide $y$ by $1$ .

$y = \frac{12}{- 6} + \frac{- 2 x}{- 6}$

Simplify the right side.

Simplify each term.

Divide $12$ by $- 6$ .

$y = - 2 + \frac{- 2 x}{- 6}$

Cancel the common factor of $- 2$ and $- 6$ .

Factor $- 2$ out of $- 2 x$ .

$y = - 2 + \frac{- 2 (x)}{- 6}$

Cancel the common factors.

Factor $- 2$ out of $- 6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

Reorder $- 2$ and $\frac{x}{3}$ .

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

Reorder terms.

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

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

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

$m = \frac{1}{3}$

$b = - 2$

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

Slope: $\frac{1}{3}$

y-intercept: $(0, - 2)$

Slope: $\frac{1}{3}$

y-intercept: $(0, - 2)$