Find the y-intercept x-4y+8=0

$x - 4 y + 8 = 0$

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 $x$ from both sides of the equation.

$- 4 y + 8 = - x$

Subtract $8$ from both sides of the equation.

$- 4 y = - x - 8$

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

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

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

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Dividing two negative values results in a positive value.

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

Divide $- 8$ by $- 4$ .

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

Reorder terms.

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

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