Algebra Examples

$y > 3 x - 2$ $2 y - x \leq 10$

Step 1

Graph $y > 3 x - 2$ .

Tap for more steps...

Step 1.1

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

Tap for more steps...

Step 1.1.1

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 1.1.2

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

$m = 3$

$b = - 2$

Step 1.1.3

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

Slope: $3$

y-intercept: $(0, - 2)$

Slope: $3$

y-intercept: $(0, - 2)$

Step 1.2

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $3 x - 2$ .

$y > 3 x - 2$

Step 2

Graph $2 y - x \leq 10$ .

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

Add $x$ to both sides of the inequality.

$2 y \leq 10 + x$

Step 2.1.1.2

Divide each term in $2 y \leq 10 + x$ by $2$ and simplify.

Tap for more steps...

Step 2.1.1.2.1

Divide each term in $2 y \leq 10 + x$ by $2$ .

$\frac{2 y}{2} \leq \frac{10}{2} + \frac{x}{2}$

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 $2$ .

Tap for more steps...

Step 2.1.1.2.2.1.1

Cancel the common factor.

$\frac{2 y}{2} \leq \frac{10}{2} + \frac{x}{2}$

Step 2.1.1.2.2.1.2

Divide $y$ by $1$ .

$y \leq \frac{10}{2} + \frac{x}{2}$

Step 2.1.1.2.3

Simplify the right side.

Tap for more steps...

Step 2.1.1.2.3.1

Divide $10$ by $2$ .

$y \leq 5 + \frac{x}{2}$

Step 2.1.2

Rearrange terms.

$y \leq \frac{x}{2} + 5$

Step 2.1.3

Reorder terms.

$y \leq \frac{1}{2} x + 5$

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 $y = m x + b$ .

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

$b = 5$

Step 2.2.2

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

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

y-intercept: $(0, 5)$

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

y-intercept: $(0, 5)$

Step 2.3

Graph a solid line, then shade the area below the boundary line since $y$ is less than $\frac{1}{2} x + 5$ .

$y \leq \frac{1}{2} x + 5$

Step 3

Plot each graph on the same coordinate system.

$y > 3 x - 2$

$2 y - x \leq 10$

Step 4