Rate of change
Calculate rate of change in Grade 9 algebra as the ratio Δy/Δx between two points, connecting this concept to slope of linear functions and interpreting units to understand what the rate means.
Key Concepts
Property A rate of change is a ratio that compares the change in one quantity with the change in another.
Examples A car travels from mile marker 50 to mile marker 200 in 3 hours: $\frac{200 50}{3} = \frac{150}{3} = 50$ miles per hour. The cost to rent a scooter changes from 30 dollars to 75 dollars over 3 hours: $\frac{75 30}{5 2} = \frac{45}{3} = 15$ dollars per hour.
Explanation This just means comparing how one thing changes with another, like miles per hour or dollars per day. Think of it as the 'story' behind the numbers. If your allowance goes up 5 dollars every 2 weeks, the rate of change tells you exactly how fast your fortune is growing. It is the real world speed of change!
Common Questions
What is rate of change in algebra?
Rate of change measures how much one quantity changes relative to another, calculated as (change in y) / (change in x) = Δy/Δx. For linear functions, the rate of change equals the slope and is constant throughout.
How do you calculate rate of change from a table of values?
Pick any two rows from the table. Divide the difference in y-values by the difference in x-values. For (2, 8) and (5, 17): rate of change = (17 - 8)/(5 - 2) = 9/3 = 3.
What does a rate of change of 0 or a negative rate of change mean?
A rate of change of 0 means y stays constant as x changes (horizontal line). A negative rate of change means y decreases as x increases (downward slope). The magnitude tells how steeply y changes per unit of x.