Find the Perpendicular Line m=2 , (-3,2)

$m = 2$ , $(- 3, 2)$

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

$m_{perpendicular} = - \frac{1}{2}$

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

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

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

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

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

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

Solve for $y$ .

Simplify $- \frac{1}{2} \cdot (x + 3)$ .

Rewrite.

$y - 2 = 0 + 0 - \frac{1}{2} \cdot (x + 3)$

Simplify by adding zeros.

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

Apply the distributive property.

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

Combine $x$ and $\frac{1}{2}$ .

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

Multiply $- \frac{1}{2} \cdot 3$ .

Multiply $3$ by $- 1$ .

$y - 2 = - \frac{x}{2} - 3 (\frac{1}{2})$

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

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

Move the negative in front of the fraction.

$y - 2 = - \frac{x}{2} - \frac{3}{2}$

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

Add $2$ to both sides of the equation.

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

To write $2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Combine $2$ and $\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $2$ by $2$ .

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

Add $- 3$ and $4$ .

$y = - \frac{x}{2} + \frac{1}{2}$

Reorder terms.

$y = - (\frac{1}{2} x) + \frac{1}{2}$

Remove parentheses.

$y = - \frac{1}{2} x + \frac{1}{2}$

Find the Perpendicular Line m=2 , (-3,2)

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