Graph 3y>3x+9

$3 y > 3 x + 9$

Step 1

Divide each term in $3 y > 3 x + 9$ by $3$ and simplify.

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

$\frac{3 y}{3} > \frac{3 x}{3} + \frac{9}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} > \frac{3 x}{3} + \frac{9}{3}$

Divide $y$ by $1$ .

$y > \frac{3 x}{3} + \frac{9}{3}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $3$ .

Cancel the common factor.

$y > \frac{3 x}{3} + \frac{9}{3}$

Divide $x$ by $1$ .

$y > x + \frac{9}{3}$

Divide $9$ by $3$ .

$y > x + 3$

Step 2

Use the slope-intercept form to find the slope and y-intercept.

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = 1$

$b = 3$

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $1$

y-intercept: $(0, 3)$

Slope: $1$

y-intercept: $(0, 3)$

Step 3

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $x + 3$ .

$y > x + 3$

Step 4