Algebra Examples

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

Step 1

Graph $2 x + 3 y < 6$ .

Tap for more steps...

Step 1.1

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

Tap for more steps...

Step 1.1.1

Solve for $y$ .

Tap for more steps...

Step 1.1.1.1

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

$3 y < 6 - 2 x$

Step 1.1.1.2

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

Tap for more steps...

Step 1.1.1.2.1

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

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

Step 1.1.1.2.2

Simplify the left side.

Tap for more steps...

Step 1.1.1.2.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 1.1.1.2.2.1.1

Cancel the common factor.

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

Step 1.1.1.2.2.1.2

Divide $y$ by $1$ .

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

Step 1.1.1.2.3

Simplify the right side.

Tap for more steps...

Step 1.1.1.2.3.1

Simplify each term.

Tap for more steps...

Step 1.1.1.2.3.1.1

Divide $6$ by $3$ .

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

Step 1.1.1.2.3.1.2

Move the negative in front of the fraction.

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

Step 1.1.2

Rearrange terms.

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

Step 1.1.3

Reorder terms.

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

Step 1.1.4

Remove parentheses.

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

Step 1.2

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

Tap for more steps...

Step 1.2.1

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

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

$b = 2$

Step 1.2.2

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: $(0, 2)$

Step 1.3

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 $4 x + 6 y > 24$ .

Tap for more steps...

Step 2.1

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

Tap for more steps...

Step 2.1.1

Solve for $y$ .

Tap for more steps...

Step 2.1.1.1

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

$6 y > 24 - 4 x$

Step 2.1.1.2

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

Tap for more steps...

Step 2.1.1.2.1

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

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

Step 2.1.1.2.2

Simplify the left side.

Tap for more steps...

Step 2.1.1.2.2.1

Cancel the common factor of $6$ .

Tap for more steps...

Step 2.1.1.2.2.1.1

Cancel the common factor.

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

Step 2.1.1.2.2.1.2

Divide $y$ by $1$ .

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

Step 2.1.1.2.3

Simplify the right side.

Tap for more steps...

Step 2.1.1.2.3.1

Simplify each term.

Tap for more steps...

Step 2.1.1.2.3.1.1

Divide $24$ by $6$ .

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

Step 2.1.1.2.3.1.2

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

Tap for more steps...

Step 2.1.1.2.3.1.2.1

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

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

Step 2.1.1.2.3.1.2.2

Cancel the common factors.

Tap for more steps...

Step 2.1.1.2.3.1.2.2.1

Factor $2$ out of $6$ .

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

Step 2.1.1.2.3.1.2.2.2

Cancel the common factor.

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

Step 2.1.1.2.3.1.2.2.3

Rewrite the expression.

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

Step 2.1.1.2.3.1.3

Move the negative in front of the fraction.

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

Step 2.1.2

Rearrange terms.

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

Step 2.1.3

Reorder terms.

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

Step 2.1.4

Remove parentheses.

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

Step 2.2

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

Tap for more steps...

Step 2.2.1

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

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

$b = 4$

Step 2.2.2

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: $(0, 4)$

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

y-intercept: $(0, 4)$

Step 2.3

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