Graph 4x+8y>=-24 , x+2y<12

$4 x + 8 y \geq - 24$ , $x + 2 y < 12$

Step 1

Graph $4 x + 8 y \geq - 24$ .

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

Solve for $y$ .

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

$8 y \geq - 24 - 4 x$

Divide each term in $8 y \geq - 24 - 4 x$ by $8$ and simplify.

Divide each term in $8 y \geq - 24 - 4 x$ by $8$ .

$\frac{8 y}{8} \geq \frac{- 24}{8} + \frac{- 4 x}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 y}{8} \geq \frac{- 24}{8} + \frac{- 4 x}{8}$

Divide $y$ by $1$ .

$y \geq \frac{- 24}{8} + \frac{- 4 x}{8}$

Simplify the right side.

Simplify each term.

Divide $- 24$ by $8$ .

$y \geq - 3 + \frac{- 4 x}{8}$

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

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

$y \geq - 3 + \frac{4 (- x)}{8}$

Cancel the common factors.

Factor $4$ out of $8$ .

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

Cancel the common factor.

$y \geq - 3 + \frac{4 (- x)}{4 \cdot 2}$

Rewrite the expression.

$y \geq - 3 + \frac{- x}{2}$

Move the negative in front of the fraction.

$y \geq - 3 - \frac{x}{2}$

Rearrange terms.

$y \geq - \frac{x}{2} - 3$

Reorder terms.

$y \geq - (\frac{1}{2} x) - 3$

Remove parentheses.

$y \geq - \frac{1}{2} x - 3$

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

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

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

$b = - 3$

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: $(0, - 3)$

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

y-intercept: $(0, - 3)$

Graph a solid line, then shade the area above the boundary line since $y$ is greater than $- \frac{1}{2} x - 3$ .

$y \geq - \frac{1}{2} x - 3$

Step 2

Graph $x + 2 y < 12$ .

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

Solve for $y$ .

Subtract $x$ from both sides of the inequality.

$2 y < 12 - x$

Divide each term in $2 y < 12 - x$ by $2$ and simplify.

Divide each term in $2 y < 12 - x$ by $2$ .

$\frac{2 y}{2} < \frac{12}{2} + \frac{- x}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} < \frac{12}{2} + \frac{- x}{2}$

Divide $y$ by $1$ .

$y < \frac{12}{2} + \frac{- x}{2}$

Simplify the right side.

Simplify each term.

Divide $12$ by $2$ .

$y < 6 + \frac{- x}{2}$

Move the negative in front of the fraction.

$y < 6 - \frac{x}{2}$

Rearrange terms.

$y < - \frac{x}{2} + 6$

Reorder terms.

$y < - (\frac{1}{2} x) + 6$

Remove parentheses.

$y < - \frac{1}{2} x + 6$

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

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

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

$b = 6$

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: $(0, 6)$

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

y-intercept: $(0, 6)$

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $- \frac{1}{2} x + 6$ .

$y < - \frac{1}{2} x + 6$

Step 3

Plot each graph on the same coordinate system.

$4 x + 8 y \geq - 24$

$x + 2 y < 12$

Step 4

Graph 4x+8y>=-24 , x+2y<12

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