Graph 3x>=2y+4

$3 x \geq 2 y + 4$

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

Solve for $y$ .

Rewrite so $y$ is on the left side of the inequality.

$2 y + 4 \leq 3 x$

Subtract $4$ from both sides of the inequality.

$2 y \leq 3 x - 4$

Divide each term in $2 y \leq 3 x - 4$ by $2$ and simplify.

Divide each term in $2 y \leq 3 x - 4$ by $2$ .

$\frac{2 y}{2} \leq \frac{3 x}{2} + \frac{- 4}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} \leq \frac{3 x}{2} + \frac{- 4}{2}$

Divide $y$ by $1$ .

$y \leq \frac{3 x}{2} + \frac{- 4}{2}$

Simplify the right side.

Divide $- 4$ by $2$ .

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

Reorder terms.

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

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

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

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

$b = - 2$

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

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

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

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

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

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

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