What is the slope of the line through the points (0,2) and (4,6)?

• A. 1
• B. 2
• C. 0
• D. -1

Answer: (A)

Slope is the ratio of how much a line rises to how much it runs, calculated from two points as (change in y) divided by (change in x). For (0,2) and (4,6), the vertical change is 6 − 2 = 4 and the horizontal change is 4 − 0 = 4, so the slope is 4/4 = 1. This means the line rises by 1 for every 1 unit it runs. A slope of 2 would require a vertical change of 8 over a run of 4, which isn’t the case; a slope of 0 would mean no vertical change, which isn’t true here; a slope of −1 would mean the line falls as you move right, which also doesn’t fit these points.