Graph y-x+2y<=1

$y - x + 2 y \leq 1$

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

Solve for $y$ .

Add $y$ and $2 y$ .

$- x + 3 y \leq 1$

Add $x$ to both sides of the inequality.

$3 y \leq 1 + x$

Divide each term in $3 y \leq 1 + x$ by $3$ and simplify.

Divide each term in $3 y \leq 1 + x$ by $3$ .

$\frac{3 y}{3} \leq \frac{1}{3} + \frac{x}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} \leq \frac{1}{3} + \frac{x}{3}$

Divide $y$ by $1$ .

$y \leq \frac{1}{3} + \frac{x}{3}$

Rearrange terms.

$y \leq \frac{x}{3} + \frac{1}{3}$

Reorder terms.

$y \leq \frac{1}{3} x + \frac{1}{3}$

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

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

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

$b = \frac{1}{3}$

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: $(0, \frac{1}{3})$

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

y-intercept: $(0, \frac{1}{3})$

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

$y \leq \frac{1}{3} x + \frac{1}{3}$