Algebra Examples

$3 x + 6 y \leq 6$ $3 x + y \leq 9$

Step 1

Graph $3 x + 6 y \leq 6$ .

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 $3 x$ from both sides of the inequality.

$6 y \leq 6 - 3 x$

Step 1.1.1.2

Divide each term in $6 y \leq 6 - 3 x$ by $6$ and simplify.

Tap for more steps...

Step 1.1.1.2.1

Divide each term in $6 y \leq 6 - 3 x$ by $6$ .

$\frac{6 y}{6} \leq \frac{6}{6} + \frac{- 3 x}{6}$

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 $6$ .

Tap for more steps...

Step 1.1.1.2.2.1.1

Cancel the common factor.

$\frac{6 y}{6} \leq \frac{6}{6} + \frac{- 3 x}{6}$

Step 1.1.1.2.2.1.2

Divide $y$ by $1$ .

$y \leq \frac{6}{6} + \frac{- 3 x}{6}$

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 $6$ .

$y \leq 1 + \frac{- 3 x}{6}$

Step 1.1.1.2.3.1.2

Cancel the common factor of $- 3$ and $6$ .

Tap for more steps...

Step 1.1.1.2.3.1.2.1

Factor $3$ out of $- 3 x$ .

$y \leq 1 + \frac{3 (- x)}{6}$

Step 1.1.1.2.3.1.2.2

Cancel the common factors.

Tap for more steps...

Step 1.1.1.2.3.1.2.2.1

Factor $3$ out of $6$ .

$y \leq 1 + \frac{3 (- x)}{3 (2)}$

Step 1.1.1.2.3.1.2.2.2

Cancel the common factor.

$y \leq 1 + \frac{3 (- x)}{3 \cdot 2}$

Step 1.1.1.2.3.1.2.2.3

Rewrite the expression.

$y \leq 1 + \frac{- x}{2}$

Step 1.1.1.2.3.1.3

Move the negative in front of the fraction.

$y \leq 1 - \frac{x}{2}$

Step 1.1.2

Rearrange terms.

$y \leq - \frac{x}{2} + 1$

Step 1.1.3

Reorder terms.

$y \leq - (\frac{1}{2} x) + 1$

Step 1.1.4

Remove parentheses.

$y \leq - \frac{1}{2} x + 1$

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 $y = m x + b$ .

$m = - \frac{1}{2}$

$b = 1$

Step 1.2.2

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

Slope: $- \frac{1}{2}$

y-intercept: $(0, 1)$

Slope: $- \frac{1}{2}$

y-intercept: $(0, 1)$

Step 1.3

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

$y \leq - \frac{1}{2} x + 1$

Step 2

Graph $3 x + y \leq 9$ .

Tap for more steps...

Step 2.1

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

Tap for more steps...

Step 2.1.1

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

$y \leq 9 - 3 x$

Step 2.1.2

Rearrange terms.

$y \leq - 3 x + 9$

Step 2.2

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

Tap for more steps...

Step 2.2.1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 2.2.2

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

$m = - 3$

$b = 9$

Step 2.2.3

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

Slope: $- 3$

y-intercept: $(0, 9)$

Slope: $- 3$

y-intercept: $(0, 9)$

Step 2.3

Graph a solid line, then shade the area below the boundary line since $y$ is less than $- 3 x + 9$ .

$y \leq - 3 x + 9$

Step 3

Plot each graph on the same coordinate system.

$3 x + 6 y \leq 6$

$3 x + y \leq 9$

Step 4