Does a slope of 2 equal 2 units?

Answer 1

Let's see this by an example.

Find the slope m of the line that passes through the points (-3, 2) and (-2, 4).

Definition of slope:

The slope of the line that passes through distinct points (x1, y1) and (x2, y2) is

Change in y/Change in x = Rise/ Run = (y2 - y1)/(x2 - x1)

where x2 - x1 is different than 0.

Solution:

Let (x1, y1) = (-3, 2) and (x2, y2) = ( -2, 4). The slope is:

m = (y2 - y1)/(x2 - x1) = (4 - 2)/[-2 - (-3)] = 2/1 = 2

The slope of the line is 2, indicating that there is a vertical change, a rise, of 2 units for each horizontal change, a run, of 1 unit. The slope is positive, and the line rises from left to right.