In y = ax + b, adjust the slope a and the y-intercept b with the sliders. The bigger a is, the steeper the line gets; changing b shifts the line up or down.
The easiest way to see what y = ax + b actually means is to think of a piggy bank. If the bank starts with b dollars and you add a dollars every month, after x months the balance is exactly ax+b dollars. b is "the amount you already had at the start" (the y-intercept), and a is "the amount that changes with every passing unit" (the slope).
On the graph, b sets where the line crosses the y-axis, and a sets how steep the line is and which way it tilts. If a is positive, the line rises toward the upper right (your savings keep growing); if a is negative, it slopes down to the lower right (you're withdrawing a little each month). If a is exactly 0, nothing changes, so the line becomes horizontal.
The x-intercept tells you the point where y=0 — in other words, "when does the balance hit zero dollars?" Set the slider to a=0 and you can see the balance never change at all, which is exactly when the x-intercept disappears.