Graph 4x+5y>20

$4 x + 5 y > 20$

Step 1

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

Solve for $y$ .

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

$5 y > 20 - 4 x$

Divide each term in $5 y > 20 - 4 x$ by $5$ and simplify.

Divide each term in $5 y > 20 - 4 x$ by $5$ .

$\frac{5 y}{5} > \frac{20}{5} + \frac{- 4 x}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} > \frac{20}{5} + \frac{- 4 x}{5}$

Divide $y$ by $1$ .

$y > \frac{20}{5} + \frac{- 4 x}{5}$

Simplify the right side.

Simplify each term.

Divide $20$ by $5$ .

$y > 4 + \frac{- 4 x}{5}$

Move the negative in front of the fraction.

$y > 4 - \frac{4 x}{5}$

Rearrange terms.

$y > - \frac{4 x}{5} + 4$

Reorder terms.

$y > - (\frac{4}{5} x) + 4$

Remove parentheses.

$y > - \frac{4}{5} x + 4$

Step 2

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

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

$m = - \frac{4}{5}$

$b = 4$

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

Slope: $- \frac{4}{5}$

y-intercept: $(0, 4)$

Slope: $- \frac{4}{5}$

y-intercept: $(0, 4)$

Step 3

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $- \frac{4}{5} x + 4$ .

$y > - \frac{4}{5} x + 4$

Step 4