Graph 2x+4y>8

$2 x + 4 y > 8$

Step 1

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

Solve for $y$ .

Subtract $2 x$ from both sides of the inequality.

$4 y > 8 - 2 x$

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

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

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Divide $8$ by $4$ .

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

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

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

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

Cancel the common factors.

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Rearrange terms.

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

Reorder terms.

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

Remove parentheses.

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

Step 2

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

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

$m = - \frac{1}{2}$

$b = 2$

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

Slope: $- \frac{1}{2}$

y-intercept: $(0, 2)$

Slope: $- \frac{1}{2}$

y-intercept: $(0, 2)$

Step 3

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $- \frac{1}{2} x + 2$ .

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

Step 4

Graph 2x+4y>8

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