Question

What is an equation of the line that is perpendicular to y= - 4/5x +3 and passes through the point (4,12)?

Answer 1

Answer:

y = $\frac{5}{4}$ x + 7

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 = - $\frac{4}{5}$ x + 3 is in this form

with m = - $\frac{4}{5}$

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

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{-\frac{4}{5} }$ = $\frac{5}{4}$, hence

y = $\frac{5}{4}$ x + c ← is the partial equation

To find c substitute (4, 12) into the partial equation

12 = 5 + c ⇒ c = 12 - 5 = 7

y = $\frac{5}{4}$ x + 7 ← equation of perpendicular line