Graph -3x-3y>=-18 -x<=-y

$- 3 x - 3 y \geq - 18$ $- x \leq - y$

Step 1

Graph $- 3 x - 3 y \geq - 18$ .

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

Solve for $y$ .

Add $3 x$ to both sides of the inequality.

$- 3 y \geq - 18 + 3 x$

Divide each term in $- 3 y \geq - 18 + 3 x$ by $- 3$ and simplify.

Divide each term in $- 3 y \geq - 18 + 3 x$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 y}{- 3} \leq \frac{- 18}{- 3} + \frac{3 x}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} \leq \frac{- 18}{- 3} + \frac{3 x}{- 3}$

Divide $y$ by $1$ .

$y \leq \frac{- 18}{- 3} + \frac{3 x}{- 3}$

Simplify the right side.

Simplify each term.

Divide $- 18$ by $- 3$ .

$y \leq 6 + \frac{3 x}{- 3}$

Cancel the common factor of $3$ and $- 3$ .

Factor $3$ out of $3 x$ .

$y \leq 6 + \frac{3 (x)}{- 3}$

Move the negative one from the denominator of $\frac{x}{- 1}$ .

$y \leq 6 - 1 \cdot x$

Rewrite $- 1 \cdot x$ as $- x$ .

$y \leq 6 - x$

Rearrange terms.

$y \leq - x + 6$

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 $- x + 6$ .

$y \leq - x + 6$

Step 2

Graph $- x \leq - y$ .

Solve for $y$ .

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

$- y \geq - x$

Divide each term in $- y \geq - x$ by $- 1$ and simplify.

Divide each term in $- y \geq - x$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- y}{- 1} \leq \frac{- x}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} \leq \frac{- x}{- 1}$

Divide $y$ by $1$ .

$y \leq \frac{- x}{- 1}$

Simplify the right side.

Dividing two negative values results in a positive value.

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

Divide $x$ by $1$ .

$y \leq x$

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 $y = m x + b$ .

$m = 1$

$b = 0$

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

Slope: $1$

y-intercept: $(0, 0)$

Slope: $1$

y-intercept: $(0, 0)$

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

$y \leq x$

Step 3

Plot each graph on the same coordinate system.

$- 3 x - 3 y \geq - 18$

$- x \leq - y$

Step 4

Graph -3x-3y>=-18 -x<=-y

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