Equation for the tangent line

Question

Suppose f(1) = 4, and the tangent line to f at x=1 goes through the point (0,2).  Find an equation for the tangent line to f at x=1. 

Answer 1

y = mx + b

 

The line passes through (1,4) and (0,2), so its slope is

 

m = (2-4)/(0-1) = 2

 

y = 2x + b

 

Use either point to find b.  Using (0,2),

 

2 = 2(0) + b

 

b = 2

 

y = 2x + 2