The y-intercept is the point at which the line crosses the y-axis -- that is, it is the point where x=0, yielding the coordinate (0, y).
Conversely, the x-intercept is the point at which the line crosses the x-axis -- that is, it is the point where y=0, yielding the coordinate (x, 0).
The slope is the average rate of change from one point to the next on a given line. In other words, it is the ratio of the vertical change (change in y) to the horizontal change (change in x) between any 2 points on a line.
slope = vertical change / horizontal change
= change in y / change in x
= Δ y / Δ x
So for any 2 points on a line, (x1, y1) & (x2, y2), the slope is: y2 - y1 / x2 - x1