Question

A line passes through the origin and has a slope of –3. What is the equation of the line that is perpendicular to the first line and passes through the point (3, 4)?

Answer 1

a line that passes through the origin (0,0) and has a slope(m) of -3

y = mx + b
0 = -3(0) + b
0 = 0 + b
0 = b

so your equation is : y = -3x + 0

however, we are looking for perpendicular. That means that the slopes have to be negative reciprocals of each other. All that means is " flip " the slope and change the sign.
So the negative reciprocal of -3 is 1/3 (see how I flipped the slope and changed the sign)

y = mx + b
slope(m) = 1/3
(3,4)...x = 3 and y = 4
now we sub
4 = 1/3(3) + b
4 = 1 + b
4 - 1 = b
3 = b

so your perpendicular equation is : y = 1/3x + 3

Answer 2

thanks!