Hi Gianella.
If y = x, then that means where we see y, we can substitute x, because they are equal, so we can rewrite the equation y = x^{3} as x = x^{3}.
What value(s) of x satisfy x = x^{3}? Zero is one value that does, and if x isn't zero, you can divide both sides of this by x to find the other values of x that work. Remember that y = x, so your points of intersection are in the form of (x, x) for all values of x.
Hope this helps,
Stephen La Rocque.
