Linear function and is it linear?

[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!

 

[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.

 

[HallsofIvy]

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

Yes, that is correct.

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.

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.