Graph x-3y<6

Divide each term in ${\displaystyle -3y<6-x}$ by ${\displaystyle -3}$. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

Cancel the common factor of ${\displaystyle -3}$.

Simplify each term.

The slope-intercept form is ${\displaystyle y=mx+b}$, where ${\displaystyle m}$ is the slope and ${\displaystyle b}$ is the y-intercept.

Reorder ${\displaystyle -2}$ and ${\displaystyle \frac{x}{3}}$.

Reorder terms.

Find the values of ${\displaystyle m}$ and ${\displaystyle b}$ using the form ${\displaystyle y=mx+b}$.

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

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

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