Graph 7x+4y>=-32 x-y<-3

$7 x + 4 y \geq - 32$ $x - y < - 3$

Graph $7 x + 4 y \geq - 32$ .

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

Solve for $y$ .

Subtract $7 x$ from both sides of the inequality.

$4 y \geq - 32 - 7 x$

Divide each term in $4 y \geq - 32 - 7 x$ by $4$ and simplify.

Divide each term in $4 y \geq - 32 - 7 x$ by $4$ .

$\frac{4 y}{4} \geq \frac{- 32}{4} + \frac{- 7 x}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} \geq \frac{- 32}{4} + \frac{- 7 x}{4}$

Divide $y$ by $1$ .

$y \geq \frac{- 32}{4} + \frac{- 7 x}{4}$

Simplify the right side.

Simplify each term.

Divide $- 32$ by $4$ .

$y \geq - 8 + \frac{- 7 x}{4}$

Move the negative in front of the fraction.

$y \geq - 8 - \frac{7 x}{4}$

Rearrange terms.

$y \geq - \frac{7 x}{4} - 8$

Reorder terms.

$y \geq - (\frac{7}{4} x) - 8$

Remove parentheses.

$y \geq - \frac{7}{4} x - 8$

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

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

$m = - \frac{7}{4}$

$b = - 8$

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

Slope: $- \frac{7}{4}$

y-intercept: $(0, - 8)$

Slope: $- \frac{7}{4}$

y-intercept: $(0, - 8)$

Graph a solid line, then shade the area above the boundary line since $y$ is greater than $- \frac{7}{4} x - 8$ .

$y \geq - \frac{7}{4} x - 8$

Graph $x - y < - 3$ .

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

Solve for $y$ .

Subtract $x$ from both sides of the inequality.

$- y < - 3 - x$

Divide each term in $- y < - 3 - x$ by $- 1$ and simplify.

Divide each term in $- y < - 3 - x$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- y}{- 1} > \frac{- 3}{- 1} + \frac{- x}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} > \frac{- 3}{- 1} + \frac{- x}{- 1}$

Divide $y$ by $1$ .

$y > \frac{- 3}{- 1} + \frac{- x}{- 1}$

Simplify the right side.

Simplify each term.

Divide $- 3$ by $- 1$ .

$y > 3 + \frac{- x}{- 1}$

Dividing two negative values results in a positive value.

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

Divide $x$ by $1$ .

$y > 3 + x$

Rearrange terms.

$y > x + 3$

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 $x + 3$ .

$y > x + 3$

Plot each graph on the same coordinate system.

$7 x + 4 y \geq - 32$

$x - y < - 3$

Graph 7x+4y>=-32 x-y<-3

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