Question

Is y a function of x? 9y-3x-4=0

Answer 1

In other words, can 9y - 3x - 4 = 0 be solved for y, and, if so, is there always exactly one y value for every input (x) value?

9y = 3x + 4
Thus, y = (3/9)x + 4, or    y = (1/3)x + 4

No matter which real x you choose, y is always assigned exactly one value by this rule.  So, yes, this is a function.