Find the y-intercept 6x-3y+6=0

$6 x - 3 y + 6 = 0$

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.

$y = m x + b$

Move all terms not containing $y$ to the right side of the equation.

Subtract $6 x$ from both sides of the equation.

$- 3 y + 6 = - 6 x$

Subtract $6$ from both sides of the equation.

$- 3 y = - 6 x - 6$

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

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

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

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

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

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

$y = \frac{- 3 (2 x)}{- 3} + \frac{- 6}{- 3}$

Cancel the common factors.

Factor $- 3$ out of $- 3$ .

$y = \frac{- 3 (2 x)}{- 3 (1)} + \frac{- 6}{- 3}$

Cancel the common factor.

$y = \frac{- 3 (2 x)}{- 3 \cdot 1} + \frac{- 6}{- 3}$

Rewrite the expression.

$y = \frac{2 x}{1} + \frac{- 6}{- 3}$

Divide $2 x$ by $1$ .

$y = 2 x + \frac{- 6}{- 3}$

Divide $- 6$ by $- 3$ .

$y = 2 x + 2$

Step 2

Using the slope-intercept form, the y-intercept is $2$ .

$b = 2$

Step 3

y-intercept in point form.

$(0, 2)$

Step 4