Precalculus Examples

$y = - \frac{1}{2} + 2$ , $(- 2, 2)$

Step 1

Find the slope when $y = - \frac{1}{2} + 2$ .

Tap for more steps...

Step 1.1

Rewrite in slope-intercept form.

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

Simplify the right side.

Tap for more steps...

Step 1.1.2.1

Simplify $- \frac{1}{2} + 2$ .

Tap for more steps...

Step 1.1.2.1.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = - \frac{1}{2} + 2 \cdot \frac{2}{2}$

Step 1.1.2.1.2

Combine $2$ and $\frac{2}{2}$ .

$y = - \frac{1}{2} + \frac{2 \cdot 2}{2}$

Step 1.1.2.1.3

Combine the numerators over the common denominator.

$y = \frac{- 1 + 2 \cdot 2}{2}$

Step 1.1.2.1.4

Simplify the numerator.

Tap for more steps...

Step 1.1.2.1.4.1

Multiply $2$ by $2$ .

$y = \frac{- 1 + 4}{2}$

Step 1.1.2.1.4.2

Add $- 1$ and $4$ .

$y = \frac{3}{2}$

Step 1.2

Using the slope-intercept form, the slope is $0$ .

$m = 0$

Step 2

The perpendicular line is vertical and the slope is undefined.

$x = - 2$

Step 3