Graph 1/2x-2y>-6

$\frac{1}{2} x - 2 y > - 6$

Step 1

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

Solve for $y$ .

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

$\frac{x}{2} - 2 y > - 6$

Subtract $\frac{x}{2}$ from both sides of the inequality.

$- 2 y > - 6 - \frac{x}{2}$

Divide each term in $- 2 y > - 6 - \frac{x}{2}$ by $- 2$ and simplify.

Divide each term in $- 2 y > - 6 - \frac{x}{2}$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 y}{- 2} < \frac{- 6}{- 2} + \frac{- \frac{x}{2}}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} < \frac{- 6}{- 2} + \frac{- \frac{x}{2}}{- 2}$

Divide $y$ by $1$ .

$y < \frac{- 6}{- 2} + \frac{- \frac{x}{2}}{- 2}$

Simplify the right side.

Simplify each term.

Divide $- 6$ by $- 2$ .

$y < 3 + \frac{- \frac{x}{2}}{- 2}$

Multiply the numerator by the reciprocal of the denominator.

$y < 3 - \frac{x}{2} \cdot \frac{1}{- 2}$

Move the negative in front of the fraction.

$y < 3 - \frac{x}{2} (- \frac{1}{2})$

Multiply $- \frac{x}{2} (- \frac{1}{2})$ .

Multiply $- 1$ by $- 1$ .

$y < 3 + 1 \frac{x}{2} \frac{1}{2}$

Multiply $\frac{x}{2}$ by $1$ .

$y < 3 + \frac{x}{2} \cdot \frac{1}{2}$

Multiply $\frac{x}{2}$ by $\frac{1}{2}$ .

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

Multiply $2$ by $2$ .

$y < 3 + \frac{x}{4}$

Rearrange terms.

$y < \frac{x}{4} + 3$

Reorder terms.

$y < \frac{1}{4} x + 3$

Step 2

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

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

$m = \frac{1}{4}$

$b = 3$

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

Slope: $\frac{1}{4}$

y-intercept: $(0, 3)$

Slope: $\frac{1}{4}$

y-intercept: $(0, 3)$

Step 3

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $\frac{1}{4} x + 3$ .

$y < \frac{1}{4} x + 3$

Step 4

Graph 1/2x-2y>-6

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