Graph 9x+4y<8 -3x-7y>=5

$9 x + 4 y < 8$ $- 3 x - 7 y \geq 5$

Graph $9 x + 4 y < 8$ .

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

Solve for $y$ .

Subtract $9 x$ from both sides of the inequality.

$4 y < 8 - 9 x$

Divide each term in $4 y < 8 - 9 x$ by $4$ and simplify.

Divide each term in $4 y < 8 - 9 x$ by $4$ .

$\frac{4 y}{4} < \frac{8}{4} + \frac{- 9 x}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} < \frac{8}{4} + \frac{- 9 x}{4}$

Divide $y$ by $1$ .

$y < \frac{8}{4} + \frac{- 9 x}{4}$

Simplify the right side.

Simplify each term.

Divide $8$ by $4$ .

$y < 2 + \frac{- 9 x}{4}$

Move the negative in front of the fraction.

$y < 2 - \frac{9 x}{4}$

Rearrange terms.

$y < - \frac{9 x}{4} + 2$

Reorder terms.

$y < - (\frac{9}{4} x) + 2$

Remove parentheses.

$y < - \frac{9}{4} x + 2$

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

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

$m = - \frac{9}{4}$

$b = 2$

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

Slope: $- \frac{9}{4}$

y-intercept: $(0, 2)$

Slope: $- \frac{9}{4}$

y-intercept: $(0, 2)$

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $- \frac{9}{4} x + 2$ .

$y < - \frac{9}{4} x + 2$

Graph $- 3 x - 7 y \geq 5$ .

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

Solve for $y$ .

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

$- 7 y \geq 5 + 3 x$

Divide each term in $- 7 y \geq 5 + 3 x$ by $- 7$ and simplify.

Divide each term in $- 7 y \geq 5 + 3 x$ by $- 7$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 7 y}{- 7} \leq \frac{5}{- 7} + \frac{3 x}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 y}{- 7} \leq \frac{5}{- 7} + \frac{3 x}{- 7}$

Divide $y$ by $1$ .

$y \leq \frac{5}{- 7} + \frac{3 x}{- 7}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y \leq - \frac{5}{7} + \frac{3 x}{- 7}$

Move the negative in front of the fraction.

$y \leq - \frac{5}{7} - \frac{3 x}{7}$

Rearrange terms.

$y \leq - \frac{3 x}{7} - \frac{5}{7}$

Reorder terms.

$y \leq - (\frac{3}{7} x) - \frac{5}{7}$

Remove parentheses.

$y \leq - \frac{3}{7} x - \frac{5}{7}$

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

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

$m = - \frac{3}{7}$

$b = - \frac{5}{7}$

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

Slope: $- \frac{3}{7}$

y-intercept: $(0, - \frac{5}{7})$

Slope: $- \frac{3}{7}$

y-intercept: $(0, - \frac{5}{7})$

Graph a solid line, then shade the area below the boundary line since $y$ is less than $- \frac{3}{7} x - \frac{5}{7}$ .

$y \leq - \frac{3}{7} x - \frac{5}{7}$

Plot each graph on the same coordinate system.

$9 x + 4 y < 8$

$- 3 x - 7 y \geq 5$

Graph 9x+4y<8 -3x-7y>=5

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