Finite Math Examples

$y = - \frac{8}{7} x + 1$

Step 1

Choose a point that the perpendicular line will pass through.

$(0, 0)$

Step 2

Find the slope when $y = - \frac{8}{7} x + 1$ .

Tap for more steps...

Step 2.1

Rewrite in slope-intercept form.

Tap for more steps...

Step 2.1.1

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 2.1.2

Simplify the right side.

Tap for more steps...

Step 2.1.2.1

Simplify each term.

Tap for more steps...

Step 2.1.2.1.1

Combine $x$ and $\frac{8}{7}$ .

$y = - \frac{x \cdot 8}{7} + 1$

Step 2.1.2.1.2

Move $8$ to the left of $x$ .

$y = - \frac{8 x}{7} + 1$

Step 2.1.3

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

Tap for more steps...

Step 2.1.3.1

Reorder terms.

$y = - (\frac{8}{7} x) + 1$

Step 2.1.3.2

Remove parentheses.

$y = - \frac{8}{7} x + 1$

Step 2.2

Using the slope-intercept form, the slope is $- \frac{8}{7}$ .

$m = - \frac{8}{7}$

Step 3

The equation of a perpendicular line must have a slope that is the negative reciprocal of the original slope.

$m_{perpendicular} = - \frac{1}{- \frac{8}{7}}$

Step 4

Simplify $- \frac{1}{- \frac{8}{7}}$ to find the slope of the perpendicular line.

Tap for more steps...

Step 4.1

Cancel the common factor of $1$ and $- 1$ .

Tap for more steps...

Step 4.1.1

Rewrite $1$ as $- 1 (- 1)$ .

$m_{perpendicular} = - \frac{- 1 \cdot - 1}{- \frac{8}{7}}$

Step 4.1.2

Move the negative in front of the fraction.

$m_{perpendicular} = \frac{1}{\frac{8}{7}}$

Step 4.2

Multiply the numerator by the reciprocal of the denominator.

$m_{perpendicular} = 1 (\frac{7}{8})$

Step 4.3

Multiply $\frac{7}{8}$ by $1$ .

$m_{perpendicular} = \frac{7}{8}$

Step 4.4

Multiply $- - \frac{7}{8}$ .

Tap for more steps...

Step 4.4.1

Multiply $- 1$ by $- 1$ .

$m_{perpendicular} = 1 (\frac{7}{8})$

Step 4.4.2

Multiply $\frac{7}{8}$ by $1$ .

$m_{perpendicular} = \frac{7}{8}$

Step 5

Find the equation of the perpendicular line using the point-slope formula.

Tap for more steps...

Step 5.1

Use the slope $\frac{7}{8}$ and a given point $(0, 0)$ to substitute for $x_{1}$ and $y_{1}$ in the point-slope form $y - y_{1} = m (x - x_{1})$ , which is derived from the slope equation $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (0) = \frac{7}{8} \cdot (x - (0))$

Step 5.2

Simplify the equation and keep it in point-slope form.

$y + 0 = \frac{7}{8} \cdot (x + 0)$

Step 6

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

Tap for more steps...

Step 6.1

Solve for $y$ .

Tap for more steps...

Step 6.1.1

Add $y$ and $0$ .

$y = \frac{7}{8} \cdot (x + 0)$

Step 6.1.2

Simplify $\frac{7}{8} \cdot (x + 0)$ .

Tap for more steps...

Step 6.1.2.1

Add $x$ and $0$ .

$y = \frac{7}{8} \cdot x$

Step 6.1.2.2

Combine $\frac{7}{8}$ and $x$ .

$y = \frac{7 x}{8}$

Step 6.2

Reorder terms.

$y = \frac{7}{8} x$

Step 7