Question

Suppose f is a linear function such that f(1) = -1 and f(3)=2. Then f(4)=?

Answer 1

Since it's linear, the slope is constant. In particular, the slope from x=1 to x=4 is the same as the slope from x=1 to x=3:

(f(4)-f(1))/(4-1) = ((f(3)-f(1))/(3-1)
(f(4)-(-1)/3 = (2-(-1))/2
f(4)+1 = 3*3/2
f(4) = 7/2

Or, you can think of it this way. Since f(x) grew by 3 when x grew by 2, f(x) will grow by 3*(3/2) when x grows by 3. -1+9/2 = 7/2