What do the slope and x-intercept represent?

If your equation is y = mx + b, then m is the slope and b is the y-intercept. Slope is equal to the change in y divided by the change in x. If you pick a point along a line (x1, y1) and a second along the same line (x2, y2), the slope is then (y2 - y1) / (x2 - x1).

As for the x-intercept, it tends to be more useful when dealing with quadratics like y = xx + x + 1. The x-intercepts can be used to simplify the formula.
Example:
y = xx -4
x-intercepts are x1 = 2 and x2 = -2
y = (x - x1)(x - x2)
y = (x - 2)( x + 2)