Find the y-intercept 4x-3y=12

$4 x - 3 y = 12$

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.

$y = m x + b$

Subtract $4 x$ from both sides of the equation.

$- 3 y = 12 - 4 x$

Divide each term in $- 3 y = 12 - 4 x$ by $- 3$ and simplify.

Divide each term in $- 3 y = 12 - 4 x$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{12}{- 3} + \frac{- 4 x}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{12}{- 3} + \frac{- 4 x}{- 3}$

Divide $y$ by $1$ .

$y = \frac{12}{- 3} + \frac{- 4 x}{- 3}$

Simplify the right side.

Simplify each term.

Divide $12$ by $- 3$ .

$y = - 4 + \frac{- 4 x}{- 3}$

Dividing two negative values results in a positive value.

$y = - 4 + \frac{4 x}{3}$

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

Reorder $- 4$ and $\frac{4 x}{3}$ .

$y = \frac{4 x}{3} - 4$

Reorder terms.

$y = \frac{4}{3} x - 4$

Step 2

Using the slope-intercept form, the y-intercept is $- 4$ .

$b = - 4$

Step 3

y-intercept in point form.

$(0, - 4)$

Step 4