Question

Find the equation of a line perpendicular to y=−4x−1 that contains the point (−2,2). Write the equation in slope-intercept form.

Answer 1

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 4x - 1 ← is in slope- intercept form

with slope m = - 4

Given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{-4}$ = $\frac{1}{4}$, thus

y = $\frac{1}{4}$ x + c ← is the partial equation of the line

To find c substitute (- 2, 2) into the partial equation

2 = - $\frac{1}{2}$ + c ⇒ c = $\frac{5}{2}$

y = $\frac{1}{4}$ x + $\frac{5}{2}$ ← in slope- intercept form