If line l in the x-y plane contains the point (-2,1),(4,5) and (5,t), what is the value of t?

Answer 1

Using the two-point form of a line:

(t-5)/(5-4) = (t-1)/(5+2)

t-5 = (t-1)/7
7t-35 = t-1
6t = 34
t = 17/3

You can see this by noting the slope of the line is 2/3.
So, as x increases by 1 from 4 to 5, y increases by 2/3 from 5 to 17/3.