# Linear function and is it linear?

1. Sep 23, 2007

### multicalcprob

I had to find an equation of a linear function z=c+mx+ny whose graph intersects the xy plane in the line y=2x+2 and contains the point (1,2,2)

I got the answer as z=2x-y+2

Now I have to see if the function f which satisfies f(0,0)=0, f(2,0)=3 and f(5,0)=6 linear? and explain it.

I have no clue what to do now. Can anyone help me? Thanks!

2. Sep 23, 2007

### bjornberntson

You need to find the vectors between the three points given and take the cross product of them. Use this resulting vector and one of the given points, you can determine the equation of a plane. If this equation satisfies all three given points, the function f is linear.
You may want to refer to http://en.wikipedia.org/wiki/Linear for the necessary explanation.

3. Sep 24, 2007

### HallsofIvy

Staff Emeritus
Yes, that is correct.

do (0,0,0), (2,0,3) and (5,0,6) lie on a straight line? If so the vectors form (0,0,0) to (2,0,3) and from (0,0,0) to (5,0,6) must be parallel. That means one vector must be a multiple of the other.