Graph 3y>=9/2x

$3 y \geq \frac{9}{2} x$

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

Divide each term in $3 y \geq \frac{9}{2} x$ by $3$ and simplify.

Divide each term in $3 y \geq \frac{9}{2} x$ by $3$ .

$\frac{3 y}{3} \geq \frac{\frac{9}{2} x}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} \geq \frac{\frac{9}{2} x}{3}$

Divide $y$ by $1$ .

$y \geq \frac{\frac{9}{2} x}{3}$

Simplify the right side.

Combine $\frac{9}{2}$ and $x$ .

$y \geq \frac{\frac{9 x}{2}}{3}$

Multiply the numerator by the reciprocal of the denominator.

$y \geq \frac{9 x}{2} \cdot \frac{1}{3}$

Cancel the common factor of $3$ .

Factor $3$ out of $9 x$ .

$y \geq \frac{3 (3 x)}{2} \cdot \frac{1}{3}$

Cancel the common factor.

$y \geq \frac{3 (3 x)}{2} \cdot \frac{1}{3}$

Rewrite the expression.

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

Reorder terms.

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

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

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

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

$b = 0$

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: $(0, 0)$

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

y-intercept: $(0, 0)$

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

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