Explain why the graph of f(x) = x+a cannot be tangent to the graph of g(x) = 4-2x, reguardless of value of a?

Answer 1

First of all, the slope of f(x) = x+ a is 1, and the slope of g(x) = 4 - 2x is -2. The slopes would have to be the same.
Next, each function is a straight line. These lines cannot be tangent, only colinear; and these are not.

Answer 2

slope of f(x) = x + 1 is +1, slope of g(x) = 4 - 2x is -2. The lines intersect at 1 point. It wouldn't make sense for a line to be tangent to a line anyway.