Any two parallel lines always have the same slope (but different y intercepts)
The equation of the green line is y = (8/5)x+6
The equation of the red line is y = (8/5)x-3
Slope intercept form is y = mx+b with m as the slope and b as the y intercept.
The slopes must be the same so that each time the line goes up some amount, we move to the right the same amount. Think of a set of stairs to possibly visualize what I mean. If the slopes are different (even slightly), then the lines will intersect at some point and we wouldn't have parallel lines.
