Find the y-intercept 7x-4y=8

$7 x - 4 y = 8$

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 $7 x$ from both sides of the equation.

$- 4 y = 8 - 7 x$

Divide each term in $- 4 y = 8 - 7 x$ by $- 4$ and simplify.

Divide each term in $- 4 y = 8 - 7 x$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{8}{- 4} + \frac{- 7 x}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{8}{- 4} + \frac{- 7 x}{- 4}$

Divide $y$ by $1$ .

$y = \frac{8}{- 4} + \frac{- 7 x}{- 4}$

Simplify the right side.

Simplify each term.

Divide $8$ by $- 4$ .

$y = - 2 + \frac{- 7 x}{- 4}$

Dividing two negative values results in a positive value.

$y = - 2 + \frac{7 x}{4}$

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

Reorder $- 2$ and $\frac{7 x}{4}$ .

$y = \frac{7 x}{4} - 2$

Reorder terms.

$y = \frac{7}{4} x - 2$

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