if f is a linear function so that f(a-1)=8 and f(a+3)=16 then find f(a)

Answer 1

Since f(a-1) = 8 and f(a+3) = 16, the points (a-1, 8) and (a+3, 16) are points on a line.

Slope of the line = (16-8) / [(a+3) - (a - 1)] = 8/4 = 2

Using the points (a, f(a)) and (a-1, 8), we have: slope = (8 - f(a)) / [(a-1) - a] = 2

8 - f(a) = -2

f(a) = 10