Question

Line s passes through the points (2, 7) and (6, 1). Line t passes through the point (5, 2) and is perpendicular to line s. What is the equation for line t?

Answer 1

line s:
if you insert both points into the standard form y=mx+b you receive
I:7=2m+b
II:1=6m+b
subtraction of II from I to eliminate b:
7-1=2m+b-4m-b
6=-4m
m=-6/4=-3/2=-1.5

to get the slope of s you have to know that for slopes of two perpendicular lines this relationship holdes:
m1*m2=-1
if we insert the slope of s:
-1.5*m2=-1
-3/2m2=-1
m2=3/2

line t therefore is y=3/2x+b
to get b we insert the point (5,2)
2=3*5/2+b
2=7.5+b
-5.5=b
-> t: y=3/2x-5.5