Precalculus Examples

$y = x - 2$ , $(2, 6)$

Use the slope-intercept form to find the slope.

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The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

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

$m = 1$

The equation of a perpendicular line to $y = x - 2$ must have a slope that is the negative reciprocal of the original slope.

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

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

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Divide $1$ by $1$ to get $1$ .

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

Multiply $- 1$ by $1$ to get $- 1$ .

$m_{perpendicular} = - 1$

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

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Find the value of $b$ using the formula for the equation of a line.

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Use the formula for the equation of a line to find $b$ .

$y = m x + b$

Substitute the value of $m$ into the equation.

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

Substitute the value of $x$ into the equation.

$y = (- 1) \cdot (2) + b$

Substitute the value of $y$ into the equation.

$(6) = (- 1) \cdot (2) + b$

Find the value of $b$ .

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Rewrite the equation as $(- 1) \cdot (2) + b = 6$ .

$(- 1) \cdot (2) + b = 6$

Simplify each term.

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Multiply $- 1$ by $2$ to get $(- 1) (2)$ .

$(- 1) (2) + b = 6$

Multiply $- 1$ by $2$ to get $- 2$ .

$- 2 + b = 6$

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

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Since $- 2$ does not contain the variable to solve for, move it to the right side of the equation by adding $2$ to both sides.

$b = 2 + 6$

Add $2$ and $6$ to get $8$ .

$b = 8$

Now that the values of $m$ (slope) and $b$ (y-intercept) are known, substitute them into $y = m x + b$ to find the equation of the line.

$y = - x + 8$

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