Rate of change

Definition

Rate of change measures how one quantity changes in relation to another. In algebra, it often refers to the slope of a line, indicating how the dependent variable changes with respect to the independent variable.

5 Must Know Facts For Your Next Test

1. The rate of change is calculated as $\Delta y / \Delta x$, where $\Delta y$ is the change in the dependent variable and $\Delta x$ is the change in the independent variable.
2. A positive rate of change indicates an increasing relationship between variables, while a negative rate of change indicates a decreasing relationship.
3. In linear functions, the rate of change is constant and equal to the slope $m$ in the equation $y = mx + b$.
4. The units of rate of change depend on the units of both variables involved; for example, if $y$ represents distance and $x$ represents time, then the rate is measured in distance per time (e.g., meters per second).
5. Understanding rates of change is essential for interpreting and modeling real-world phenomena using linear functions.

Review Questions

• How do you calculate the rate of change between two points on a graph?
• What does a negative rate of change indicate about the behavior of a function?
• In the equation $y = mx + b$, what role does $m$ play?

Related terms

Slope: The measure of steepness or incline of a line, defined as rise over run ($\Delta y / \Delta x$).

Linear Function: A function that creates a straight line when graphed and can be expressed in the form $y = mx + b$.

Dependent Variable: The output variable in a function, typically represented by $y$, whose value depends on that of another variable.