Precalculus Examples

$y = x - 2$

Step 1

Choose a point that the perpendicular line will pass through.

$(0, 0)$

Step 2

Use the slope-intercept form to find the slope.

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Step 2.1

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 2.2

Using the slope-intercept form, the slope is $1$ .

$m = 1$

Step 3

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

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

Step 4

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

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Step 4.1

Cancel the common factor of $1$ .

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Step 4.1.1

Cancel the common factor.

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

Step 4.1.2

Rewrite the expression.

$m_{perpendicular} = - 1 \cdot 1$

Step 4.2

Multiply $- 1$ by $1$ .

$m_{perpendicular} = - 1$

Step 5

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

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Step 5.1

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

$y - (0) = - 1 \cdot (x - (0))$

Step 5.2

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

$y + 0 = - 1 \cdot (x + 0)$

Step 6

Solve for $y$ .

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Step 6.1

Add $y$ and $0$ .

$y = - 1 \cdot (x + 0)$

Step 6.2

Simplify $- 1 \cdot (x + 0)$ .

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Step 6.2.1

Add $x$ and $0$ .

$y = - 1 \cdot x$

Step 6.2.2

Rewrite $- 1 x$ as $- x$ .

$y = - x$

Step 7

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