Find the Perpendicular Line y+5=-(x+4) , (-8,2)

$y + 5 = - (x + 4)$ , $(- 8, 2)$

Solve $y + 5 = - (x + 4)$ .

Simplify $- (x + 4)$ .

Rewrite.

$y + 5 = 0 + 0 - (x + 4)$

Simplify by adding zeros.

$y + 5 = - (x + 4)$

Apply the distributive property.

$y + 5 = - x - 1 \cdot 4$

Multiply $- 1$ by $4$ .

$y + 5 = - x - 4$

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

Subtract $5$ from both sides of the equation.

$y = - x - 4 - 5$

Subtract $5$ from $- 4$ .

$y = - x - 9$

Use the slope-intercept form to find the slope.

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 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.

Divide $1$ by $- 1$ .

$m_{perpendicular} = 1$

Multiply $- 1$ by $- 1$ .

$m_{perpendicular} = 1$

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

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

$y - (2) = 1 \cdot (x - (- 8))$

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

$y - 2 = 1 \cdot (x + 8)$

Solve for $y$ .

Multiply $x + 8$ by $1$ .

$y - 2 = x + 8$

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

Add $2$ to both sides of the equation.

$y = x + 8 + 2$

Add $8$ and $2$ .

$y = x + 10$

Find the Perpendicular Line y+5=-(x+4) , (-8,2)

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