Question

Find the equation of the line described.

Answer 1

Answer:

y = - $\frac{1}{3}$ x + $\frac{19}{3}$

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 = 3x + 6 ← is in slope- intercept form

with slope m = 3

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

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

y = - $\frac{1}{3}$ x + c ← is the partial equation

To find c , substitute (4, 5) into the partial equation

5 = - $\frac{4}{3}$ + c ⇒ c = 5 + $\frac{4}{3}$ = $\frac{19}{3}$

y = - $\frac{1}{3}$ x + $\frac{19}{3}$ ← equation of perpendicular line