Question

Find the equation of the line that is perpendicular to y = –3x + 1 and passes though the point (6, 3).

Answer 1

Answer:

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

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 + 1 ← 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

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

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

To find c substitute (6, 3) into the partial equation

3 = 2 + c ⇒ c = 3 - 2 = 1

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