What term describes the rate at which one quantity changes in relation to another?

The term that describes the rate at which one quantity changes in relation to another is "slope." In the context of algebra and coordinate geometry, the slope is a measure of how steep a line is, which quantitatively describes how much the dependent variable (usually represented on the y-axis) changes for a given change in the independent variable (usually represented on the x-axis).

For example, in the equation of a line expressed as ( y = mx + b ), the ( m ) represents the slope. A higher slope value indicates a steeper incline, meaning a larger change in ( y ) for each unit change in ( x ). Conversely, a slope of zero indicates a horizontal line where there is no change in ( y ) regardless of changes in ( x ).

Understanding slope is fundamental in analyzing linear relationships, making it a critical concept in various applications, including physics, economics, and statistics, where rates of change are essential to interpreting data relationships.