Graph 2x+5y>-6 -4x+3y<=2

$2 x + 5 y > - 6$ $- 4 x + 3 y \leq 2$

Step 1

Graph $2 x + 5 y > - 6$ .

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

Solve for $y$ .

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

$5 y > - 6 - 2 x$

Divide each term in $5 y > - 6 - 2 x$ by $5$ and simplify.

Divide each term in $5 y > - 6 - 2 x$ by $5$ .

$\frac{5 y}{5} > \frac{- 6}{5} + \frac{- 2 x}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} > \frac{- 6}{5} + \frac{- 2 x}{5}$

Divide $y$ by $1$ .

$y > \frac{- 6}{5} + \frac{- 2 x}{5}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y > - \frac{6}{5} + \frac{- 2 x}{5}$

Move the negative in front of the fraction.

$y > - \frac{6}{5} - \frac{2 x}{5}$

Rearrange terms.

$y > - \frac{2 x}{5} - \frac{6}{5}$

Reorder terms.

$y > - (\frac{2}{5} x) - \frac{6}{5}$

Remove parentheses.

$y > - \frac{2}{5} x - \frac{6}{5}$

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

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

$m = - \frac{2}{5}$

$b = - \frac{6}{5}$

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

Slope: $- \frac{2}{5}$

y-intercept: $(0, - \frac{6}{5})$

Slope: $- \frac{2}{5}$

y-intercept: $(0, - \frac{6}{5})$

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $- \frac{2}{5} x - \frac{6}{5}$ .

$y > - \frac{2}{5} x - \frac{6}{5}$

Step 2

Graph $- 4 x + 3 y \leq 2$ .

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

Solve for $y$ .

Add $4 x$ to both sides of the inequality.

$3 y \leq 2 + 4 x$

Divide each term in $3 y \leq 2 + 4 x$ by $3$ and simplify.

Divide each term in $3 y \leq 2 + 4 x$ by $3$ .

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Rearrange terms.

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

Reorder terms.

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

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

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

$m = \frac{4}{3}$

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

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

Slope: $\frac{4}{3}$

y-intercept: $(0, \frac{2}{3})$

Slope: $\frac{4}{3}$

y-intercept: $(0, \frac{2}{3})$

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

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

Step 3

Plot each graph on the same coordinate system.

$2 x + 5 y > - 6$

$- 4 x + 3 y \leq 2$

Step 4

Graph 2x+5y>-6 -4x+3y<=2

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