Graph 2x-3y<12 y<=-x+6

$2 x - 3 y < 12$ $y \leq - x + 6$

Graph $2 x - 3 y < 12$ .

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

Solve for $y$ .

Subtract $2 x$ from both sides of the inequality.

$- 3 y < 12 - 2 x$

Divide each term in $- 3 y < 12 - 2 x$ by $- 3$ and simplify.

Divide each term in $- 3 y < 12 - 2 x$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 y}{- 3} > \frac{12}{- 3} + \frac{- 2 x}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} > \frac{12}{- 3} + \frac{- 2 x}{- 3}$

Divide $y$ by $1$ .

$y > \frac{12}{- 3} + \frac{- 2 x}{- 3}$

Simplify the right side.

Simplify each term.

Divide $12$ by $- 3$ .

$y > - 4 + \frac{- 2 x}{- 3}$

Dividing two negative values results in a positive value.

$y > - 4 + \frac{2 x}{3}$

Rearrange terms.

$y > \frac{2 x}{3} - 4$

Reorder terms.

$y > \frac{2}{3} x - 4$

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

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

$m = \frac{2}{3}$

$b = - 4$

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

Slope: $\frac{2}{3}$

y-intercept: $(0, - 4)$

Slope: $\frac{2}{3}$

y-intercept: $(0, - 4)$

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $\frac{2}{3} x - 4$ .

$y > \frac{2}{3} x - 4$

Graph $y \leq - x + 6$ .

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

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

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

$m = - 1$

$b = 6$

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

Slope: $- 1$

y-intercept: $(0, 6)$

Slope: $- 1$

y-intercept: $(0, 6)$

Graph a solid line, then shade the area below the boundary line since $y$ is less than $- x + 6$ .

$y \leq - x + 6$

Plot each graph on the same coordinate system.

$2 x - 3 y < 12$

$y \leq - x + 6$

Graph 2x-3y<12 y<=-x+6

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