Definition: The rate of change describes how fast one quantity changes compared with another, found by dividing the change in output by the change in input.
What is the rate of change?
It compares how much y changes for each unit change in x. For a line, it is constant and equals the slope.
How do you compute it?
Rate of change = change in y / change in x. A plant is 8 cm tall at week 2 and 29 cm at week 5. The change in height is 21 cm over 3 weeks, so the rate is 7 cm per week.
What does the sign tell?
A positive rate means growth, a negative rate means decline. A phone battery going from 80 percent to 50 percent in 2 hours has rate -15 percent per hour.
Is it always constant?
Not for every function. A table with rates 3, 5, 7 between rows is changing at different speeds, so the function is nonlinear.
How does it relate to tables and graphs?
In a table, compute the rate for several pairs. If all match, the function is linear. On a graph, a steeper line means a larger magnitude of rate.
What is a common mistake?
Computing x over y. Always keep track of which quantity is the output. Also keep units: dollars per hour, not hours per dollar.
Where to learn it
- Modeling Real Situations With Linear Functions – lesson
- Slope and Proportional Relationships on Graphs – lesson