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

$3 x + 4 y = 12$

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 $3 x$ from both sides of the equation.

$4 y = 12 - 3 x$

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

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

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Divide $12$ by $4$ .

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

Move the negative in front of the fraction.

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

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

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

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

Reorder terms.

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

Remove parentheses.

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

Step 2

Using the slope-intercept form, the y-intercept is $3$ .

$b = 3$

Step 3

y-intercept in point form.

$(0, 3)$

Step 4