Which description best matches the slope's definition?

Which description best matches the slope's definition?

• A. Rise/Run
• B. Vertical Change / Horizontal Change
• C. Area under the curve
• D. Distance between points

Answer: (B)

Slope is the rate at which y changes as x changes. It’s the ratio of how much the vertical position changes to how much the horizontal position changes, written as Δy/Δx. Saying it as vertical change over horizontal change makes the idea of “how steep” or “how fast y grows with x” very clear. The other ideas describe different things: area under a curve relates to accumulation or integration, and distance between points measures length, not a rate of change. Rise over run is basically another way to express the same idea, but the phrasing that emphasizes vertical change and horizontal change captures the exact meaning of the slope as a ratio of changes in y to changes in x.

Slope is the rate at which y changes as x changes. It’s the ratio of how much the vertical position changes to how much the horizontal position changes, written as Δy/Δx. Saying it as vertical change over horizontal change makes the idea of “how steep” or “how fast y grows with x” very clear. The other ideas describe different things: area under a curve relates to accumulation or integration, and distance between points measures length, not a rate of change. Rise over run is basically another way to express the same idea, but the phrasing that emphasizes vertical change and horizontal change captures the exact meaning of the slope as a ratio of changes in y to changes in x.