Graph 4x+3y>-6 x-3y<=-9

$4 x + 3 y > - 6$ $x - 3 y \leq - 9$

Step 1

Graph $4 x + 3 y > - 6$ .

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

Solve for $y$ .

Subtract $4 x$ from both sides of the inequality.

$3 y > - 6 - 4 x$

Divide each term in $3 y > - 6 - 4 x$ by $3$ and simplify.

Divide each term in $3 y > - 6 - 4 x$ by $3$ .

$\frac{3 y}{3} > \frac{- 6}{3} + \frac{- 4 x}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} > \frac{- 6}{3} + \frac{- 4 x}{3}$

Divide $y$ by $1$ .

$y > \frac{- 6}{3} + \frac{- 4 x}{3}$

Simplify the right side.

Simplify each term.

Divide $- 6$ by $3$ .

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

Move the negative in front of the fraction.

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

Rearrange terms.

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

Reorder terms.

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

Remove parentheses.

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

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

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

$m = - \frac{4}{3}$

$b = - 2$

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

Slope: $- \frac{4}{3}$

y-intercept: $(0, - 2)$

Slope: $- \frac{4}{3}$

y-intercept: $(0, - 2)$

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

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

Step 2

Graph $x - 3 y \leq - 9$ .

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

Solve for $y$ .

Subtract $x$ from both sides of the inequality.

$- 3 y \leq - 9 - x$

Divide each term in $- 3 y \leq - 9 - x$ by $- 3$ and simplify.

Divide each term in $- 3 y \leq - 9 - x$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 y}{- 3} \geq \frac{- 9}{- 3} + \frac{- x}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} \geq \frac{- 9}{- 3} + \frac{- x}{- 3}$

Divide $y$ by $1$ .

$y \geq \frac{- 9}{- 3} + \frac{- x}{- 3}$

Simplify the right side.

Simplify each term.

Divide $- 9$ by $- 3$ .

$y \geq 3 + \frac{- x}{- 3}$

Dividing two negative values results in a positive value.

$y \geq 3 + \frac{x}{3}$

Rearrange terms.

$y \geq \frac{x}{3} + 3$

Reorder terms.

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

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

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

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

$b = 3$

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: $(0, 3)$

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

y-intercept: $(0, 3)$

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

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

Step 3

Plot each graph on the same coordinate system.

$4 x + 3 y > - 6$

$x - 3 y \leq - 9$

Step 4

Graph 4x+3y>-6 x-3y<=-9

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