Graph 3x-2y<=-1 x+4y>=-12

$3 x - 2 y \leq - 1$ $x + 4 y \geq - 12$

Step 1

Graph $3 x - 2 y \leq - 1$ .

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

Solve for $y$ .

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

$- 2 y \leq - 1 - 3 x$

Divide each term in $- 2 y \leq - 1 - 3 x$ by $- 2$ and simplify.

Divide each term in $- 2 y \leq - 1 - 3 x$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

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

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Dividing two negative values results in a positive value.

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

Dividing two negative values results in a positive value.

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

Rearrange terms.

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

Reorder terms.

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

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

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

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

$b = \frac{1}{2}$

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: $(0, \frac{1}{2})$

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

y-intercept: $(0, \frac{1}{2})$

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

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

Step 2

Graph $x + 4 y \geq - 12$ .

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

Solve for $y$ .

Subtract $x$ from both sides of the inequality.

$4 y \geq - 12 - x$

Divide each term in $4 y \geq - 12 - x$ by $4$ and simplify.

Divide each term in $4 y \geq - 12 - x$ by $4$ .

$\frac{4 y}{4} \geq \frac{- 12}{4} + \frac{- x}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} \geq \frac{- 12}{4} + \frac{- x}{4}$

Divide $y$ by $1$ .

$y \geq \frac{- 12}{4} + \frac{- x}{4}$

Simplify the right side.

Simplify each term.

Divide $- 12$ by $4$ .

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

Move the negative in front of the fraction.

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

Rearrange terms.

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

Reorder terms.

$y \geq - (\frac{1}{4} x) - 3$

Remove parentheses.

$y \geq - \frac{1}{4} x - 3$

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

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

$m = - \frac{1}{4}$

$b = - 3$

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

Slope: $- \frac{1}{4}$

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

Slope: $- \frac{1}{4}$

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

Graph a solid line, then shade the area above the boundary line since $y$ is greater than $- \frac{1}{4} x - 3$ .

$y \geq - \frac{1}{4} x - 3$

Step 3

Plot each graph on the same coordinate system.

$3 x - 2 y \leq - 1$

$x + 4 y \geq - 12$

Step 4

Graph 3x-2y<=-1 x+4y>=-12

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