Find the Perpendicular Line through: (-5,3) , perp. to y=-5x+5

through: $(- 5, 3)$ , perp. to $y = - 5 x + 5$

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 $- 5$ .

$m = - 5$

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

$m_{perpendicular} = - \frac{1}{- 5}$

Simplify $- \frac{1}{- 5}$ to find the slope of the perpendicular line.

Move the negative in front of the fraction.

$m_{perpendicular} = \frac{1}{5}$

Multiply $- - \frac{1}{5}$ .

Multiply $- 1$ by $- 1$ .

$m_{perpendicular} = 1 (\frac{1}{5})$

Multiply $\frac{1}{5}$ by $1$ .

$m_{perpendicular} = \frac{1}{5}$

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

Use the slope $\frac{1}{5}$ and a given point $(- 5, 3)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (3) = \frac{1}{5} \cdot (x - (- 5))$

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

$y - 3 = \frac{1}{5} \cdot (x + 5)$

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

Solve for $y$ .

Simplify $\frac{1}{5} \cdot (x + 5)$ .

Rewrite.

$y - 3 = 0 + 0 + \frac{1}{5} \cdot (x + 5)$

Simplify by adding zeros.

$y - 3 = \frac{1}{5} \cdot (x + 5)$

Apply the distributive property.

$y - 3 = \frac{1}{5} x + \frac{1}{5} \cdot 5$

Combine $\frac{1}{5}$ and $x$ .

$y - 3 = \frac{x}{5} + \frac{1}{5} \cdot 5$

Cancel the common factor of $5$ .

Cancel the common factor.

$y - 3 = \frac{x}{5} + \frac{1}{5} \cdot 5$

Rewrite the expression.

$y - 3 = \frac{x}{5} + 1$

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

Add $3$ to both sides of the equation.

$y = \frac{x}{5} + 1 + 3$

Add $1$ and $3$ .

$y = \frac{x}{5} + 4$

Reorder terms.

$y = \frac{1}{5} x + 4$

Find the Perpendicular Line through: (-5,3) , perp. to y=-5x+5

Related Questions

Support LCMGCF.com by disabling your adblocker.