Pre-Algebra Examples

$4 y > 2 x + 12$

Step 1

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

Tap for more steps...

Step 1.1

Divide each term in $4 y > 2 x + 12$ by $4$ and simplify.

Tap for more steps...

Step 1.1.1

Divide each term in $4 y > 2 x + 12$ by $4$ .

$\frac{4 y}{4} > \frac{2 x}{4} + \frac{12}{4}$

Step 1.1.2

Simplify the left side.

Tap for more steps...

Step 1.1.2.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 1.1.2.1.1

Cancel the common factor.

$\frac{4 y}{4} > \frac{2 x}{4} + \frac{12}{4}$

Step 1.1.2.1.2

Divide $y$ by $1$ .

$y > \frac{2 x}{4} + \frac{12}{4}$

Step 1.1.3

Simplify the right side.

Tap for more steps...

Step 1.1.3.1

Simplify each term.

Tap for more steps...

Step 1.1.3.1.1

Cancel the common factor of $2$ and $4$ .

Tap for more steps...

Step 1.1.3.1.1.1

Factor $2$ out of $2 x$ .

$y > \frac{2 (x)}{4} + \frac{12}{4}$

Step 1.1.3.1.1.2

Cancel the common factors.

Tap for more steps...

Step 1.1.3.1.1.2.1

Factor $2$ out of $4$ .

$y > \frac{2 x}{2 \cdot 2} + \frac{12}{4}$

Step 1.1.3.1.1.2.2

Cancel the common factor.

$y > \frac{2 x}{2 \cdot 2} + \frac{12}{4}$

Step 1.1.3.1.1.2.3

Rewrite the expression.

$y > \frac{x}{2} + \frac{12}{4}$

Step 1.1.3.1.2

Divide $12$ by $4$ .

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

Step 1.2

Reorder terms.

$y > \frac{1}{2} x + 3$

Step 2

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

Tap for more steps...

Step 2.1

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

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

$b = 3$

Step 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: $(0, 3)$

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

y-intercept: $(0, 3)$

Step 3

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $\frac{1}{2} x + 3$ .

$y > \frac{1}{2} x + 3$

Step 4