What is slope?

• A. The rate of change of a line; rise over run.
• B. The y-intercept value in y = mx + b.
• C. The distance around a circle.
• D. The center point of a circle.

Answer: (A)

Slope is how steep a line is, describing how much y changes as x changes. It’s the rate of change, written as rise over run (the change in y divided by the change in x). For example, if you go up 3 units for every 2 units you move to the right, the slope is 3/2. A line with a positive slope rises as you move to the right; a negative slope falls; a slope of zero means the line is horizontal; an undefined slope occurs for a vertical line. In the equation y = mx + b, the letter m represents this rate of change. The other ideas described—where the line crosses the y-axis (y-intercept), the distance around a circle (circumference), and the circle’s center—are different concepts, so describing slope as rise over run is the correct interpretation.