Graph 3x+2y<=6 x-2y<=2

$3 x + 2 y \leq 6$ $x - 2 y \leq 2$

Graph $3 x + 2 y \leq 6$ .

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

Solve for $y$ .

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

$2 y \leq 6 - 3 x$

Divide each term in $2 y \leq 6 - 3 x$ by $2$ and simplify.

Divide each term in $2 y \leq 6 - 3 x$ by $2$ .

$\frac{2 y}{2} \leq \frac{6}{2} + \frac{- 3 x}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} \leq \frac{6}{2} + \frac{- 3 x}{2}$

Divide $y$ by $1$ .

$y \leq \frac{6}{2} + \frac{- 3 x}{2}$

Simplify the right side.

Simplify each term.

Divide $6$ by $2$ .

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

Move the negative in front of the fraction.

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

Rearrange terms.

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

Reorder terms.

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

Remove parentheses.

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

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

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

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

$b = 3$

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: $(0, 3)$

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

y-intercept: $(0, 3)$

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

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

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 $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

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

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Divide $2$ by $- 2$ .

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

Dividing two negative values results in a positive value.

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

Rearrange terms.

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

Reorder terms.

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

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 above the boundary line since $y$ is greater than $\frac{1}{2} x - 1$ .

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

Plot each graph on the same coordinate system.

$3 x + 2 y \leq 6$

$x - 2 y \leq 2$

Graph 3x+2y<=6 x-2y<=2

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