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

$x - 3 y = 6$

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 $x$ from both sides of the equation.

$- 3 y = 6 - x$

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

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

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

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Divide $6$ by $- 3$ .

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

Dividing two negative values results in a positive value.

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

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: $(0, - 2)$