Algebra Examples

y = - 0.75 x

$y = - 0.75 x$

(8, 0)

$(8, 0)$

Step 1

Use the slope-intercept form to find the slope.

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Step 1.1

The slope-intercept form is

y = m x + b

$y = m x + b$ , where

m

$m$ is the slope and

b

$b$ is the y-intercept.

y = m x + b

$y = m x + b$

Step 1.2

Using the slope-intercept form, the slope is

- 0.75

$- 0.75$ .

m = - 0.75

$m = - 0.75$

m = - 0.75

$m = - 0.75$

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}{- 0.75}

$m_{perpendicular} = - \frac{1}{- 0.75}$

Step 3

Simplify

- \frac{1}{- 0.75}

$- \frac{1}{- 0.75}$ to find the slope of the perpendicular line.

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Step 3.1

Divide

1

$1$ by

- 0.75

$- 0.75$ .

m_{perpendicular} = 1. ¯ 3

$m_{perpendicular} = 1.\overline{3}$

Step 3.2

Multiply

- 1

$- 1$ by

- 1. ¯ 3

$- 1.\overline{3}$ .

m_{perpendicular} = 1. ¯ 3

$m_{perpendicular} = 1.\overline{3}$

m_{perpendicular} = 1. ¯ 3

$m_{perpendicular} = 1.\overline{3}$

Step 4

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

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Step 4.1

Use the slope

1. ¯ 3

$1.\overline{3}$ and a given point

(8, 0)

$(8, 0)$ to substitute for

x_{1}

$x_{1}$ and

y_{1}

$y_{1}$ in the point-slope form

y - y_{1} = m (x - x_{1})

$y - y_{1} = m (x - x_{1})$ , which is derived from the slope equation

m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

y - (0) = 1. ¯ 3 \cdot (x - (8))

$y - (0) = 1.\overline{3} \cdot (x - (8))$

Step 4.2

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

y + 0 = 1. ¯ 3 \cdot (x - 8)

$y + 0 = 1.\overline{3} \cdot (x - 8)$

y + 0 = 1. ¯ 3 \cdot (x - 8)

$y + 0 = 1.\overline{3} \cdot (x - 8)$

Step 5

Solve for

y

$y$ .

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Step 5.1

Add

y

$y$ and

0

$0$ .

y = 1. ¯ 3 \cdot (x - 8)

$y = 1.\overline{3} \cdot (x - 8)$

Step 5.2

Simplify

1. ¯ 3 \cdot (x - 8)

$1.\overline{3} \cdot (x - 8)$ .

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Step 5.2.1

Apply the distributive property.

y = 1. ¯ 3 x + 1. ¯ 3 \cdot - 8

$y = 1.\overline{3} x + 1.\overline{3} \cdot - 8$

Step 5.2.2

Multiply

$1.\overline{3}$ by

$- 8$ .

$y = 1.\overline{3} x - 10.\overline{6}$

Step 6