Question

what does f '(1) equal if the line tangent to the graph function f has a point at (1,7) and passes through point (-2,-2)?

Answer 1

First you must find an equation given two point (1, 7) and (-2, -2).
y2-y1/x2-x1 = m
m=3 (slope)
y=3x+b (gives you general point slope formula
(7) = 3(1) + b (plug in a point to find y intercept, b)
b=4
gives you the function y=3x+4
f' = 3
therefore f'(1) = 3