Graph 3y>=2x-6

$3 y \geq 2 x - 6$

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

Divide each term in $3 y \geq 2 x - 6$ by $3$ and simplify.

Divide each term in $3 y \geq 2 x - 6$ by $3$ .

$\frac{3 y}{3} \geq \frac{2 x}{3} + \frac{- 6}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} \geq \frac{2 x}{3} + \frac{- 6}{3}$

Divide $y$ by $1$ .

$y \geq \frac{2 x}{3} + \frac{- 6}{3}$

Simplify the right side.

Divide $- 6$ by $3$ .

$y \geq \frac{2 x}{3} - 2$

Reorder terms.

$y \geq \frac{2}{3} x - 2$

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

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

$m = \frac{2}{3}$

$b = - 2$

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

Slope: $\frac{2}{3}$

y-intercept: $(0, - 2)$

Slope: $\frac{2}{3}$

y-intercept: $(0, - 2)$

Graph a solid line, then shade the area above the boundary line since $y$ is greater than $\frac{2}{3} x - 2$ .

$y \geq \frac{2}{3} x - 2$