Using the slope formula m = (y2 - y1) / (x2 - x1), what is the slope of the line through (2, 3) and (5, 11)?

• A. 8/3
• B. 3/8
• C. 1/2
• D. 5/3

Answer: (A)

The slope measures how steep a line is by comparing how much you go up (the rise) to how much you move to the right (the run) between two points on the line. Using the two points (2, 3) and (5, 11), the rise is 11 − 3 = 8 and the run is 5 − 2 = 3. So the slope is m = 8/3.

This means for every 3 units you move to the right, you go up 8 units. The other fractions would come from using different changes that don’t match these two points, so they don’t reflect the actual rise and run here.