Question

Carlos enters 10 into a function machine and gets 8. Then he enters 15 into the machine and gets 9. What rule does the function machine use when a number is entered into it?

Answer 1

Try just a straight line. You can do little else with just two points.

y = m x + b

8 = m (10) + b
9 = m (15) + b

-1 = -5 m
m = 1/5
b = 9 - 3 = 6

so
f(x) = x/5 + 6