Graph y<-x-2y

$y < - x - 2 y$

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 $2 y$ to both sides of the inequality.

$y + 2 y < - x$

Add $y$ and $2 y$ .

$3 y < - x$

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

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

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

Reorder terms.

$y < - (\frac{1}{3} x)$

Remove parentheses.

$y < - \frac{1}{3} x$

Step 2

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

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

$m = - \frac{1}{3}$

$b = 0$

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

Slope: $- \frac{1}{3}$

y-intercept: $(0, 0)$

Slope: $- \frac{1}{3}$

y-intercept: $(0, 0)$

Step 3

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $- \frac{1}{3} x$ .

$y < - \frac{1}{3} x$

Step 4