Graph -9x+5y<=-6 4x-8y<-16

$- 9 x + 5 y \leq - 6$ $4 x - 8 y < - 16$

Graph $- 9 x + 5 y \leq - 6$ .

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

Solve for $y$ .

Add $9 x$ to both sides of the inequality.

$5 y \leq - 6 + 9 x$

Divide each term in $5 y \leq - 6 + 9 x$ by $5$ and simplify.

Divide each term in $5 y \leq - 6 + 9 x$ by $5$ .

$\frac{5 y}{5} \leq \frac{- 6}{5} + \frac{9 x}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} \leq \frac{- 6}{5} + \frac{9 x}{5}$

Divide $y$ by $1$ .

$y \leq \frac{- 6}{5} + \frac{9 x}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$y \leq - \frac{6}{5} + \frac{9 x}{5}$

Rearrange terms.

$y \leq \frac{9 x}{5} - \frac{6}{5}$

Reorder terms.

$y \leq \frac{9}{5} x - \frac{6}{5}$

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

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

$m = \frac{9}{5}$

$b = - \frac{6}{5}$

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

Slope: $\frac{9}{5}$

y-intercept: $(0, - \frac{6}{5})$

Slope: $\frac{9}{5}$

y-intercept: $(0, - \frac{6}{5})$

Graph a solid line, then shade the area below the boundary line since $y$ is less than $\frac{9}{5} x - \frac{6}{5}$ .

$y \leq \frac{9}{5} x - \frac{6}{5}$

Graph $4 x - 8 y < - 16$ .

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

Solve for $y$ .

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

$- 8 y < - 16 - 4 x$

Divide each term in $- 8 y < - 16 - 4 x$ by $- 8$ and simplify.

Divide each term in $- 8 y < - 16 - 4 x$ by $- 8$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 8 y}{- 8} > \frac{- 16}{- 8} + \frac{- 4 x}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 y}{- 8} > \frac{- 16}{- 8} + \frac{- 4 x}{- 8}$

Divide $y$ by $1$ .

$y > \frac{- 16}{- 8} + \frac{- 4 x}{- 8}$

Simplify the right side.

Simplify each term.

Divide $- 16$ by $- 8$ .

$y > 2 + \frac{- 4 x}{- 8}$

Cancel the common factor of $- 4$ and $- 8$ .

Factor $- 4$ out of $- 4 x$ .

$y > 2 + \frac{- 4 (x)}{- 8}$

Cancel the common factors.

Factor $- 4$ out of $- 8$ .

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

Cancel the common factor.

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

Rewrite the expression.

$y > 2 + \frac{x}{2}$

Rearrange terms.

$y > \frac{x}{2} + 2$

Reorder terms.

$y > \frac{1}{2} x + 2$

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

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

$m = \frac{1}{2}$

$b = 2$

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

Slope: $\frac{1}{2}$

y-intercept: $(0, 2)$

Slope: $\frac{1}{2}$

y-intercept: $(0, 2)$

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $\frac{1}{2} x + 2$ .

$y > \frac{1}{2} x + 2$

Plot each graph on the same coordinate system.

$- 9 x + 5 y \leq - 6$

$4 x - 8 y < - 16$

Graph -9x+5y<=-6 4x-8y<-16

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