Graph x+3<y 3x-3y>=12

$x + 3 < y$ $3 x - 3 y \geq 12$

Graph $x + 3 < y$ .

Rewrite so $y$ is on the left side of the inequality.

$y > x + 3$

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 $y = m x + b$ .

$m = 1$

$b = 3$

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

Slope: $1$

y-intercept: $(0, 3)$

Slope: $1$

y-intercept: $(0, 3)$

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $x + 3$ .

$y > x + 3$

Graph $3 x - 3 y \geq 12$ .

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

Solve for $y$ .

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

$- 3 y \geq 12 - 3 x$

Divide each term in $- 3 y \geq 12 - 3 x$ by $- 3$ and simplify.

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

$\frac{- 3 y}{- 3} \leq \frac{12}{- 3} + \frac{- 3 x}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} \leq \frac{12}{- 3} + \frac{- 3 x}{- 3}$

Divide $y$ by $1$ .

$y \leq \frac{12}{- 3} + \frac{- 3 x}{- 3}$

Simplify the right side.

Simplify each term.

Divide $12$ by $- 3$ .

$y \leq - 4 + \frac{- 3 x}{- 3}$

Cancel the common factor of $- 3$ .

Cancel the common factor.

$y \leq - 4 + \frac{- 3 x}{- 3}$

Divide $x$ by $1$ .

$y \leq - 4 + x$

Rearrange terms.

$y \leq x - 4$

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 $y = m x + b$ .

$m = 1$

$b = - 4$

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

Slope: $1$

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

Slope: $1$

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

Graph a solid line, then shade the area below the boundary line since $y$ is less than $x - 4$ .

$y \leq x - 4$

Plot each graph on the same coordinate system.

$x + 3 < y$

$3 x - 3 y \geq 12$

Graph x+3<y 3x-3y>=12

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