Question

F(0)=2, f(2)=4, linear equation?

Answer 1

If you separate those into points (0,2) and (2,4) then figure out the slope by using the equation y2-y1 divided by x2-x1, you'll get 4-2 over 2-0 which gives you 2/2 or 1. You found the slope so you can plug that into the slope-intercept equation y-y1=m(x-x1). For you, it'd be y-2=1(x-0), you end up with the equation y=x+2.

Answer 2

Could be, but not necessarily.

You have two points on the graph:    (0, 2)  and  (2, 4) .

Yes, there's a straight line that could go through those two points.  Y = x + 2 .

But there are a million other graphs that could go through the same two points.
You could draw ellipses, parabolas, circles, exponentials etc. that all go through
them.  So when you only know two points on the graph, you can't really tell what
the equation has to be, or whether or not it's linear.