Pre-Algebra Examples

$y = 9 x - 8$ , $(6, - 4)$

Step 1

Use the slope-intercept form to find the slope.

Tap for more steps...

Step 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 1.2

Using the slope-intercept form, the slope is $9$ .

$m = 9$

Step 2

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

$m_{perpendicular} = - \frac{1}{9}$

Step 3

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

Tap for more steps...

Step 3.1

Use the slope $- \frac{1}{9}$ and a given point $(6, - 4)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 4) = - \frac{1}{9} \cdot (x - (6))$

Step 3.2

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

$y + 4 = - \frac{1}{9} \cdot (x - 6)$

Step 4

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

Tap for more steps...

Step 4.1

Solve for $y$ .

Tap for more steps...

Step 4.1.1

Simplify $- \frac{1}{9} \cdot (x - 6)$ .

Tap for more steps...

Step 4.1.1.1

Rewrite.

$y + 4 = 0 + 0 - \frac{1}{9} \cdot (x - 6)$

Step 4.1.1.2

Simplify by adding zeros.

$y + 4 = - \frac{1}{9} \cdot (x - 6)$

Step 4.1.1.3

Apply the distributive property.

$y + 4 = - \frac{1}{9} x - \frac{1}{9} \cdot - 6$

Step 4.1.1.4

Combine $x$ and $\frac{1}{9}$ .

$y + 4 = - \frac{x}{9} - \frac{1}{9} \cdot - 6$

Step 4.1.1.5

Cancel the common factor of $3$ .

Tap for more steps...

Step 4.1.1.5.1

Move the leading negative in $- \frac{1}{9}$ into the numerator.

$y + 4 = - \frac{x}{9} + \frac{- 1}{9} \cdot - 6$

Step 4.1.1.5.2

Factor $3$ out of $9$ .

$y + 4 = - \frac{x}{9} + \frac{- 1}{3 (3)} \cdot - 6$

Step 4.1.1.5.3

Factor $3$ out of $- 6$ .

$y + 4 = - \frac{x}{9} + \frac{- 1}{3 \cdot 3} \cdot (3 \cdot - 2)$

Step 4.1.1.5.4

Cancel the common factor.

$y + 4 = - \frac{x}{9} + \frac{- 1}{3 \cdot 3} \cdot (3 \cdot - 2)$

Step 4.1.1.5.5

Rewrite the expression.

$y + 4 = - \frac{x}{9} + \frac{- 1}{3} \cdot - 2$

Step 4.1.1.6

Combine $\frac{- 1}{3}$ and $- 2$ .

$y + 4 = - \frac{x}{9} + \frac{- - 2}{3}$

Step 4.1.1.7

Multiply $- 1$ by $- 2$ .

$y + 4 = - \frac{x}{9} + \frac{2}{3}$

Step 4.1.2

Move all terms not containing $y$ to the right side of the equation.

Tap for more steps...

Step 4.1.2.1

Subtract $4$ from both sides of the equation.

$y = - \frac{x}{9} + \frac{2}{3} - 4$

Step 4.1.2.2

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = - \frac{x}{9} + \frac{2}{3} - 4 \cdot \frac{3}{3}$

Step 4.1.2.3

Combine $- 4$ and $\frac{3}{3}$ .

$y = - \frac{x}{9} + \frac{2}{3} + \frac{- 4 \cdot 3}{3}$

Step 4.1.2.4

Combine the numerators over the common denominator.

$y = - \frac{x}{9} + \frac{2 - 4 \cdot 3}{3}$

Step 4.1.2.5

Simplify the numerator.

Tap for more steps...

Step 4.1.2.5.1

Multiply $- 4$ by $3$ .

$y = - \frac{x}{9} + \frac{2 - 12}{3}$

Step 4.1.2.5.2

Subtract $12$ from $2$ .

$y = - \frac{x}{9} + \frac{- 10}{3}$

Step 4.1.2.6

Move the negative in front of the fraction.

$y = - \frac{x}{9} - \frac{10}{3}$

Step 4.2

Reorder terms.

$y = - (\frac{1}{9} x) - \frac{10}{3}$

Step 4.3

Remove parentheses.

$y = - \frac{1}{9} x - \frac{10}{3}$

Step 5