Algebra Examples

$y = - 0.75 x$ $(8, 0)$

Step 1

Use the slope-intercept form to find the slope.

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Step 1.1

The slope-intercept form is $y = m x + b$ , 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 $- 0.75$ .

$m = - 0.75$

Step 2

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

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

Step 3

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

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Step 3.1

Divide $1$ by $- 0.75$ .

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

Step 3.2

Multiply $- 1$ by $- 1.\overline{3}$ .

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

Step 4

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

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Step 4.1

Use the slope $1.\overline{3}$ and a given point $(8, 0)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

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

Step 4.2

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

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

Step 5

Solve for $y$ .

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Step 5.1

Add $y$ and $0$ .

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

Step 5.2

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

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Step 5.2.1

Apply the distributive property.

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

Step 5.2.2

Multiply $1.\overline{3}$ by $- 8$ .

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

Step 6