Rate of Change
Rate of change is a Grade 7 math concept from Yoshiwara Intermediate Algebra measuring how one quantity changes relative to another. For a linear function, the rate of change equals the slope and is constant. For nonlinear functions, the rate changes over different intervals.
Key Concepts
Property A rate is a type of ratio that compares two quantities with different units.
A rate of change is a special kind of ratio that compares the change in two quantities or variables.
In mathematics, we use the symbol $\Delta$ (delta) for change in . Thus, a rate of change can be expressed as the ratio of the change in one variable to the change in another: $$\text{Rate of change} = \frac{\Delta d}{\Delta t}$$.
Common Questions
What is rate of change in mathematics?
Rate of change measures how much one variable changes per unit change in another. For a function, it is (change in y)/(change in x) over an interval.
How does rate of change relate to slope?
For a linear function, the rate of change is constant and equals the slope m. For y = mx + b, slope m is the rate of change of y per unit increase in x.
How do you calculate average rate of change over an interval?
Average rate of change = (f(b) - f(a))/(b - a) for the interval [a, b].
What does a positive rate of change mean?
A positive rate of change means the quantity is increasing. A negative rate means it is decreasing.