Graph 2x+3y<6 4x+6y>24

$2 x + 3 y < 6$ $4 x + 6 y > 24$

Step 1

Graph $2 x + 3 y < 6$ .

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

Solve for $y$ .

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

$3 y < 6 - 2 x$

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

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

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Divide $6$ by $3$ .

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

Move the negative in front of the fraction.

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

Rearrange terms.

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

Reorder terms.

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

Remove parentheses.

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

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

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

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

$b = 2$

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: $(0, 2)$

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

y-intercept: $(0, 2)$

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

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

Step 2

Graph $4 x + 6 y > 24$ .

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

Solve for $y$ .

Subtract $4 x$ from both sides of the inequality.

$6 y > 24 - 4 x$

Divide each term in $6 y > 24 - 4 x$ by $6$ and simplify.

Divide each term in $6 y > 24 - 4 x$ by $6$ .

$\frac{6 y}{6} > \frac{24}{6} + \frac{- 4 x}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 y}{6} > \frac{24}{6} + \frac{- 4 x}{6}$

Divide $y$ by $1$ .

$y > \frac{24}{6} + \frac{- 4 x}{6}$

Simplify the right side.

Simplify each term.

Divide $24$ by $6$ .

$y > 4 + \frac{- 4 x}{6}$

Cancel the common factor of $- 4$ and $6$ .

Factor $2$ out of $- 4 x$ .

$y > 4 + \frac{2 (- 2 x)}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

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

Cancel the common factor.

$y > 4 + \frac{2 (- 2 x)}{2 \cdot 3}$

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Rearrange terms.

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

Reorder terms.

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

Remove parentheses.

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

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 3

Plot each graph on the same coordinate system.

$2 x + 3 y < 6$

$4 x + 6 y > 24$

Step 4

Graph 2x+3y<6 4x+6y>24

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