Find the y-intercept 4y=8x-3

$4 y = 8 x - 3$

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.

$y = m x + b$

Divide each term in $4 y = 8 x - 3$ by $4$ and simplify.

Divide each term in $4 y = 8 x - 3$ by $4$ .

$\frac{4 y}{4} = \frac{8 x}{4} + \frac{- 3}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} = \frac{8 x}{4} + \frac{- 3}{4}$

Divide $y$ by $1$ .

$y = \frac{8 x}{4} + \frac{- 3}{4}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $8$ and $4$ .

Factor $4$ out of $8 x$ .

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

Cancel the common factors.

Factor $4$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $2 x$ by $1$ .

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

Move the negative in front of the fraction.

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

Step 2

Using the slope-intercept form, the y-intercept is $- \frac{3}{4}$ .

$b = - \frac{3}{4}$

Step 3

y-intercept in point form.

$(0, - \frac{3}{4})$

Step 4