Susannah,

Yes, the function is linear. How can you tell? It's because the term with x in it is just x. If it had a term with x^{2} or x^{3}, it would curve instead of being a straight line (linear).

The equation is actually already in slope intercept form!

Besides the unknown variables x and y, there are two constants in y-mx+b, the m, which is the slope of the line, and the b, which is just a constant by itself. In this problem, m is the 3p, and b is just zero. To make it look more like mx+b, you could write it like this:

y = (3p)x + 0

The parentheses and the "+0" aren't necessary. The p is included to show you that there can be other stuff in a linear equation besides x, y, m and b. If you needed to work with this equation, the problem would have to tell you what value p has. It will just be some number. For example, a problem could ask you to graph the equation for p=2, then do it again for p=3, etc.

For example, if p=3, you would have this equation:

y = 2px

y = 2*3*x

y = 6x

I hope this helps.