Graph 4x-2y>8

$4 x - 2 y > 8$

Step 1

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

Solve for $y$ .

Subtract $4 x$ from both sides of the inequality.

$- 2 y > 8 - 4 x$

Divide each term in $- 2 y > 8 - 4 x$ by $- 2$ and simplify.

Divide each term in $- 2 y > 8 - 4 x$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 y}{- 2} < \frac{8}{- 2} + \frac{- 4 x}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} < \frac{8}{- 2} + \frac{- 4 x}{- 2}$

Divide $y$ by $1$ .

$y < \frac{8}{- 2} + \frac{- 4 x}{- 2}$

Simplify the right side.

Simplify each term.

Divide $8$ by $- 2$ .

$y < - 4 + \frac{- 4 x}{- 2}$

Cancel the common factor of $- 4$ and $- 2$ .

Factor $- 2$ out of $- 4 x$ .

$y < - 4 + \frac{- 2 (2 x)}{- 2}$

Cancel the common factors.

Factor $- 2$ out of $- 2$ .

$y < - 4 + \frac{- 2 (2 x)}{- 2 (1)}$

Cancel the common factor.

$y < - 4 + \frac{- 2 (2 x)}{- 2 \cdot 1}$

Rewrite the expression.

$y < - 4 + \frac{2 x}{1}$

Divide $2 x$ by $1$ .

$y < - 4 + 2 x$

Rearrange terms.

$y < 2 x - 4$

Step 2

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

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

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

$m = 2$

$b = - 4$

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

Slope: $2$

y-intercept: $(0, - 4)$

Slope: $2$

y-intercept: $(0, - 4)$

Step 3

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $2 x - 4$ .

$y < 2 x - 4$

Step 4

Graph 4x-2y>8

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