Graph 1/3y-1/2x>2

$\frac{1}{3} y - \frac{1}{2} x > 2$

Step 1

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

Solve for $y$ .

Simplify each term.

Combine $\frac{1}{3}$ and $y$ .

$\frac{y}{3} - \frac{1}{2} x > 2$

Combine $x$ and $\frac{1}{2}$ .

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

Add $\frac{x}{2}$ to both sides of the inequality.

$\frac{y}{3} > 2 + \frac{x}{2}$

Multiply both sides by $3$ .

$\frac{y}{3} \cdot 3 > (2 + \frac{x}{2}) \cdot 3$

Simplify.

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{y}{3} \cdot 3 > (2 + \frac{x}{2}) \cdot 3$

Rewrite the expression.

$y > (2 + \frac{x}{2}) \cdot 3$

Simplify the right side.

Simplify $(2 + \frac{x}{2}) \cdot 3$ .

Simplify terms.

Apply the distributive property.

$y > 2 \cdot 3 + \frac{x}{2} \cdot 3$

Multiply $2$ by $3$ .

$y > 6 + \frac{x}{2} \cdot 3$

Combine $\frac{x}{2}$ and $3$ .

$y > 6 + \frac{x \cdot 3}{2}$

Move $3$ to the left of $x$ .

$y > 6 + \frac{3 x}{2}$

Reorder $6$ and $\frac{3 x}{2}$ .

$y > \frac{3 x}{2} + 6$

Reorder terms.

$y > \frac{3}{2} x + 6$

Step 2

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

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

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

$b = 6$

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: $(0, 6)$

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

y-intercept: $(0, 6)$

Step 3

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $\frac{3}{2} x + 6$ .

$y > \frac{3}{2} x + 6$

Step 4

Graph 1/3y-1/2x>2

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