Find the Perpendicular Line y=5x-1 passing through (2,-4)

$y = 5 x - 1$ passing through $(2, - 4)$

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.

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

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

Use the slope $- \frac{1}{5}$ and a given point $(2, - 4)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 4) = - \frac{1}{5} \cdot (x - (2))$

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

$y + 4 = - \frac{1}{5} \cdot (x - 2)$

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

Solve for $y$ .

Simplify $- \frac{1}{5} \cdot (x - 2)$ .

Rewrite.

$y + 4 = 0 + 0 - \frac{1}{5} \cdot (x - 2)$

Simplify by adding zeros.

$y + 4 = - \frac{1}{5} \cdot (x - 2)$

Apply the distributive property.

$y + 4 = - \frac{1}{5} x - \frac{1}{5} \cdot - 2$

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

$y + 4 = - \frac{x}{5} - \frac{1}{5} \cdot - 2$

Multiply $- \frac{1}{5} \cdot - 2$ .

Multiply $- 2$ by $- 1$ .

$y + 4 = - \frac{x}{5} + 2 (\frac{1}{5})$

Combine $2$ and $\frac{1}{5}$ .

$y + 4 = - \frac{x}{5} + \frac{2}{5}$

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

Subtract $4$ from both sides of the equation.

$y = - \frac{x}{5} + \frac{2}{5} - 4$

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$y = - \frac{x}{5} + \frac{2}{5} - 4 \cdot \frac{5}{5}$

Combine $- 4$ and $\frac{5}{5}$ .

$y = - \frac{x}{5} + \frac{2}{5} + \frac{- 4 \cdot 5}{5}$

Combine the numerators over the common denominator.

$y = - \frac{x}{5} + \frac{2 - 4 \cdot 5}{5}$

Simplify the numerator.

Multiply $- 4$ by $5$ .

$y = - \frac{x}{5} + \frac{2 - 20}{5}$

Subtract $20$ from $2$ .

$y = - \frac{x}{5} + \frac{- 18}{5}$

Move the negative in front of the fraction.

$y = - \frac{x}{5} - \frac{18}{5}$

Reorder terms.

$y = - (\frac{1}{5} x) - \frac{18}{5}$

Remove parentheses.

$y = - \frac{1}{5} x - \frac{18}{5}$

Find the Perpendicular Line y=5x-1 passing through (2,-4)

Related Questions

Support LCMGCF.com by disabling your adblocker.