Question

What is the equation of the line that is perpendicular to y= -3/4x -2 and passes through the point (-12, 7)? A. Y= -3/4x -27/4 B. Y= -3/4x + 16 C. Y= 4/3x - 64/3 or D. Y= 4/3x + 23
Serious answers please!

Answer 1

Answer:

D

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 = - $\frac{3}{4}$ x - 2 ← is in slope- intercept form

with slope m = - $\frac{3}{4}$

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

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{-\frac{3}{4} }$ = $\frac{4}{3}$, thus

y = $\frac{4}{3}$ x + c ← is the partial equation of the perpendicular line

To find c substitute (- 12, 7) into the partial equation

7 = - 16 + c ⇒ c = 7 + 16 = 23

y = $\frac{4}{3}$ x + 23 → D