Graph 3y>2x+12 2x+y<=-5

$3 y > 2 x + 12$ $2 x + y \leq - 5$

Step 1

Graph $3 y > 2 x + 12$ .

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

Divide each term in $3 y > 2 x + 12$ by $3$ and simplify.

Divide each term in $3 y > 2 x + 12$ by $3$ .

$\frac{3 y}{3} > \frac{2 x}{3} + \frac{12}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} > \frac{2 x}{3} + \frac{12}{3}$

Divide $y$ by $1$ .

$y > \frac{2 x}{3} + \frac{12}{3}$

Simplify the right side.

Divide $12$ by $3$ .

$y > \frac{2 x}{3} + 4$

Reorder terms.

$y > \frac{2}{3} x + 4$

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

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

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

$b = 4$

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

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

y-intercept: $(0, 4)$

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

y-intercept: $(0, 4)$

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $\frac{2}{3} x + 4$ .

$y > \frac{2}{3} x + 4$

Step 2

Graph $2 x + y \leq - 5$ .

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

Subtract $2 x$ from both sides of the inequality.

$y \leq - 5 - 2 x$

Rearrange terms.

$y \leq - 2 x - 5$

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 $y = m x + b$ .

$m = - 2$

$b = - 5$

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

Slope: $- 2$

y-intercept: $(0, - 5)$

Slope: $- 2$

y-intercept: $(0, - 5)$

Graph a solid line, then shade the area below the boundary line since $y$ is less than $- 2 x - 5$ .

$y \leq - 2 x - 5$

Step 3

Plot each graph on the same coordinate system.

$3 y > 2 x + 12$

$2 x + y \leq - 5$

Step 4

Graph 3y>2x+12 2x+y<=-5

Related Questions

Support LCMGCF.com by disabling your adblocker.