Graph 3x+2y>=-2 x+2y<=2

$3 x + 2 y \geq - 2$ $x + 2 y \leq 2$

Step 1

Graph $3 x + 2 y \geq - 2$ .

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

Solve for $y$ .

Subtract $3 x$ from both sides of the inequality.

$2 y \geq - 2 - 3 x$

Divide each term in $2 y \geq - 2 - 3 x$ by $2$ and simplify.

Divide each term in $2 y \geq - 2 - 3 x$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Divide $- 2$ by $2$ .

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

Move the negative in front of the fraction.

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

Rearrange terms.

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

Reorder terms.

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

Remove parentheses.

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

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

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

$m = - \frac{3}{2}$

$b = - 1$

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

Slope: $- \frac{3}{2}$

y-intercept: $(0, - 1)$

Slope: $- \frac{3}{2}$

y-intercept: $(0, - 1)$

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

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

Step 2

Graph $x + 2 y \leq 2$ .

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

Solve for $y$ .

Subtract $x$ from both sides of the inequality.

$2 y \leq 2 - x$

Divide each term in $2 y \leq 2 - x$ by $2$ and simplify.

Divide each term in $2 y \leq 2 - x$ by $2$ .

$\frac{2 y}{2} \leq \frac{2}{2} + \frac{- x}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} \leq \frac{2}{2} + \frac{- x}{2}$

Divide $y$ by $1$ .

$y \leq \frac{2}{2} + \frac{- x}{2}$

Simplify the right side.

Simplify each term.

Divide $2$ by $2$ .

$y \leq 1 + \frac{- x}{2}$

Move the negative in front of the fraction.

$y \leq 1 - \frac{x}{2}$

Rearrange terms.

$y \leq - \frac{x}{2} + 1$

Reorder terms.

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

Remove parentheses.

$y \leq - \frac{1}{2} x + 1$

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

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

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

$b = 1$

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: $(0, 1)$

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

y-intercept: $(0, 1)$

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

$y \leq - \frac{1}{2} x + 1$

Step 3

Plot each graph on the same coordinate system.

$3 x + 2 y \geq - 2$

$x + 2 y \leq 2$

Step 4

Graph 3x+2y>=-2 x+2y<=2

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