Find the y-intercept 5x+6y=24

$5 x + 6 y = 24$

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 $5 x$ from both sides of the equation.

$6 y = 24 - 5 x$

Divide each term in $6 y = 24 - 5 x$ by $6$ and simplify.

Divide each term in $6 y = 24 - 5 x$ by $6$ .

$\frac{6 y}{6} = \frac{24}{6} + \frac{- 5 x}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 y}{6} = \frac{24}{6} + \frac{- 5 x}{6}$

Divide $y$ by $1$ .

$y = \frac{24}{6} + \frac{- 5 x}{6}$

Simplify the right side.

Simplify each term.

Divide $24$ by $6$ .

$y = 4 + \frac{- 5 x}{6}$

Move the negative in front of the fraction.

$y = 4 - \frac{5 x}{6}$

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

Reorder $4$ and $- \frac{5 x}{6}$ .

$y = - \frac{5 x}{6} + 4$

Reorder terms.

$y = - (\frac{5}{6} x) + 4$

Remove parentheses.

$y = - \frac{5}{6} x + 4$

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