When you change a slope from positive to negative, it flips because it goes from being an increasing slope to a decreasing slope. negative slopes decrease as they move from left to right; positive slopes increase from left to right. in the case of y = x, which is line directly through the origin, this line is steadily increasing from the bottom left corner to the top of the right corner of a graph. when you change the slope from 1 to -1, the graph instead declines from the top left to the bottom right.
