One way to calculate the slope of a line is by drawing a slope triangle. For example, using this slope triangle, the slope of the line is -42, or -21. The slope is negative because the line is decreasing from left to right.
Another way to calculate the slope of this line uses just the points A:(1,5) and B:(5,3). The slope is the vertical change divided by the horizontal change, or the change in the y-values divided by the change in the x-values. Between points A and B, the y-value change is 3−5=-2 and the x-value change is 5−1=4. This means the slope is -42, or -21, which is the same value as the slope calculated using a slope triangle.
Notice that in each of the calculations, the value from point A was subtracted from the value from point B. If it had been done the other way around, then the y-value change would have been 5−3=2 and the x-value change would have been 1−5=-4, which still gives a slope of -21.