Graph 3x+4y<x-y+2

$3 x + 4 y < x - y + 2$

Step 1

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

Solve for $y$ .

Move all terms containing $y$ to the left side of the inequality.

Add $y$ to both sides of the inequality.

$3 x + 4 y + y < x + 2$

Add $4 y$ and $y$ .

$3 x + 5 y < x + 2$

Move all terms not containing $y$ to the right side of the inequality.

Subtract $3 x$ from both sides of the inequality.

$5 y < x + 2 - 3 x$

Subtract $3 x$ from $x$ .

$5 y < - 2 x + 2$

Divide each term in $5 y < - 2 x + 2$ by $5$ and simplify.

Divide each term in $5 y < - 2 x + 2$ by $5$ .

$\frac{5 y}{5} < \frac{- 2 x}{5} + \frac{2}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} < \frac{- 2 x}{5} + \frac{2}{5}$

Divide $y$ by $1$ .

$y < \frac{- 2 x}{5} + \frac{2}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$y < - \frac{2 x}{5} + \frac{2}{5}$

Reorder terms.

$y < - (\frac{2}{5} x) + \frac{2}{5}$

Remove parentheses.

$y < - \frac{2}{5} x + \frac{2}{5}$

Step 2

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

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

$m = - \frac{2}{5}$

$b = \frac{2}{5}$

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

Slope: $- \frac{2}{5}$

y-intercept: $(0, \frac{2}{5})$

Slope: $- \frac{2}{5}$

y-intercept: $(0, \frac{2}{5})$

Step 3

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $- \frac{2}{5} x + \frac{2}{5}$ .

$y < - \frac{2}{5} x + \frac{2}{5}$

Step 4