Find the y-intercept -4x+6y-5z=60

$- 4 x + 6 y - 5 z = 60$

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.

$y = m x + b$

Move all terms not containing $y$ to the right side of the equation.

Add $4 x$ to both sides of the equation.

$6 y - 5 z = 60 + 4 x$

Add $5 z$ to both sides of the equation.

$6 y = 60 + 4 x + 5 z$

Divide each term in $6 y = 60 + 4 x + 5 z$ by $6$ and simplify.

Divide each term in $6 y = 60 + 4 x + 5 z$ by $6$ .

$\frac{6 y}{6} = \frac{60}{6} + \frac{4 x}{6} + \frac{5 z}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 y}{6} = \frac{60}{6} + \frac{4 x}{6} + \frac{5 z}{6}$

Divide $y$ by $1$ .

$y = \frac{60}{6} + \frac{4 x}{6} + \frac{5 z}{6}$

Simplify the right side.

Simplify each term.

Divide $60$ by $6$ .

$y = 10 + \frac{4 x}{6} + \frac{5 z}{6}$

Cancel the common factor of $4$ and $6$ .

Factor $2$ out of $4 x$ .

$y = 10 + \frac{2 (2 x)}{6} + \frac{5 z}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

$y = 10 + \frac{2 (2 x)}{2 (3)} + \frac{5 z}{6}$

Cancel the common factor.

$y = 10 + \frac{2 (2 x)}{2 \cdot 3} + \frac{5 z}{6}$

Rewrite the expression.

$y = 10 + \frac{2 x}{3} + \frac{5 z}{6}$

Arrange the polynomial to follow the $y = m x + b$ form for slope and y-intercept.

$y = \frac{2 x}{3} + 10$

Rewrite in slope-intercept form.

$y = \frac{2}{3} x + 10$

Using the slope-intercept form, the y-intercept is $10$ .

$b = 10$

y-intercept in point form.

$(0, 10)$