Find the y-intercept 3x-4y=-2

$3 x - 4 y = - 2$

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.

$- 4 y = - 2 - 3 x$

Divide each term in $- 4 y = - 2 - 3 x$ by $- 4$ and simplify.

Divide each term in $- 4 y = - 2 - 3 x$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{- 2}{- 4} + \frac{- 3 x}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{- 2}{- 4} + \frac{- 3 x}{- 4}$

Divide $y$ by $1$ .

$y = \frac{- 2}{- 4} + \frac{- 3 x}{- 4}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $- 2$ and $- 4$ .

Factor $- 2$ out of $- 2$ .

$y = \frac{- 2 (1)}{- 4} + \frac{- 3 x}{- 4}$

Cancel the common factors.

Factor $- 2$ out of $- 4$ .

$y = \frac{- 2 \cdot 1}{- 2 \cdot 2} + \frac{- 3 x}{- 4}$

Cancel the common factor.

$y = \frac{- 2 \cdot 1}{- 2 \cdot 2} + \frac{- 3 x}{- 4}$

Rewrite the expression.

$y = \frac{1}{2} + \frac{- 3 x}{- 4}$

Dividing two negative values results in a positive value.

$y = \frac{1}{2} + \frac{3 x}{4}$

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

Reorder $\frac{1}{2}$ and $\frac{3 x}{4}$ .

$y = \frac{3 x}{4} + \frac{1}{2}$

Reorder terms.

$y = \frac{3}{4} x + \frac{1}{2}$

Step 2

Using the slope-intercept form, the y-intercept is $\frac{1}{2}$ .

$b = \frac{1}{2}$

Step 3

y-intercept in point form.

$(0, \frac{1}{2})$

Step 4