Find the Perpendicular Line -x+y=-6 that contains the point (-4,5)

$- x + y = - 6$ that contains the point $(- 4, 5)$

Add $x$ to both sides of the equation.

$y = - 6 + x$

Find the slope when $y = - 6 + x$ .

Rewrite in slope-intercept form.

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

$y = m x + b$

Reorder $- 6$ and $x$ .

$y = x - 6$

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.

Cancel the common factor of $1$ .

Cancel the common factor.

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

Rewrite the expression.

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

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 $(- 4, 5)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (5) = - 1 \cdot (x - (- 4))$

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

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

Solve for $y$ .

Simplify $- 1 \cdot (x + 4)$ .

Rewrite.

$y - 5 = 0 + 0 - 1 \cdot (x + 4)$

Simplify by adding zeros.

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

Apply the distributive property.

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

Simplify the expression.

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

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

Multiply $- 1$ by $4$ .

$y - 5 = - x - 4$

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

Add $5$ to both sides of the equation.

$y = - x - 4 + 5$

Add $- 4$ and $5$ .

$y = - x + 1$

Find the Perpendicular Line -x+y=-6 that contains the point (-4,5)

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