Graph -4x+5y<-3

$- 4 x + 5 y < - 3$

Step 1

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

Solve for $y$ .

Add $4 x$ to both sides of the inequality.

$5 y < - 3 + 4 x$

Divide each term in $5 y < - 3 + 4 x$ by $5$ and simplify.

Divide each term in $5 y < - 3 + 4 x$ by $5$ .

$\frac{5 y}{5} < \frac{- 3}{5} + \frac{4 x}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} < \frac{- 3}{5} + \frac{4 x}{5}$

Divide $y$ by $1$ .

$y < \frac{- 3}{5} + \frac{4 x}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$y < - \frac{3}{5} + \frac{4 x}{5}$

Rearrange terms.

$y < \frac{4 x}{5} - \frac{3}{5}$

Reorder terms.

$y < \frac{4}{5} x - \frac{3}{5}$

Step 2

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

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

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

$b = - \frac{3}{5}$

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: $(0, - \frac{3}{5})$

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

y-intercept: $(0, - \frac{3}{5})$

Step 3

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $\frac{4}{5} x - \frac{3}{5}$ .

$y < \frac{4}{5} x - \frac{3}{5}$

Step 4