Find the y-intercept 3y=9x+6

$3 y = 9 x + 6$

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 $3 y = 9 x + 6$ by $3$ and simplify.

Divide each term in $3 y = 9 x + 6$ by $3$ .

$\frac{3 y}{3} = \frac{9 x}{3} + \frac{6}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{9 x}{3} + \frac{6}{3}$

Divide $y$ by $1$ .

$y = \frac{9 x}{3} + \frac{6}{3}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $9$ and $3$ .

Factor $3$ out of $9 x$ .

$y = \frac{3 (3 x)}{3} + \frac{6}{3}$

Cancel the common factors.

Factor $3$ out of $3$ .

$y = \frac{3 (3 x)}{3 (1)} + \frac{6}{3}$

Cancel the common factor.

$y = \frac{3 (3 x)}{3 \cdot 1} + \frac{6}{3}$

Rewrite the expression.

$y = \frac{3 x}{1} + \frac{6}{3}$

Divide $3 x$ by $1$ .

$y = 3 x + \frac{6}{3}$

Divide $6$ by $3$ .

$y = 3 x + 2$

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