It would be better if you state which part(s) of the explanation you don't understand. You are given two points on the graph of the function:
(70,50) and (100,100)
As HallsofIvy pointed out, there are an infinite number of functions we could find passing through those two points, but the simplest of these is going to be a linear function (\(n\) points can be uniquely described by a polynomial of degree \(n-1\)). Using the definition of slope, and the point-slope equation for a line, we then find:
[MATH]f(x)=\frac{100-50}{100-70}(x-70)+50=\frac{5}{3}x-70\cdot\frac{5}{3}+50=\frac{5}{3}x-\frac{200}{3}=\frac{5}{3}(x-40)[/MATH]