Constant rate of change
Key notes:
🔹 What is Constant Rate of Change?
It means a quantity changes by the same amount every time 📊.
👉 The change is steady and predictable.
🔹 Simple Meaning 🧠
If one value goes up (or down), the other value changes equally each time ➕➖.
🔹 Real-Life Examples 🌍
🚶 Walking at the same speed
💰 Saving ₹100 every week
🚗 A car moving 60 km every hour
All these show a constant rate of change ✔️
🔹 In Tables 📋
If the difference between numbers is always the same, the rate is constant.
Example:
2, 4, 6, 8 → increases by +2 each time ➕➕
🔹 In Graphs 📉
📍 A straight line shows a constant rate of change
📍 The line can go upward ⬆️ or downward ⬇️
🔹 Positive vs Negative Rate 🔄
➕ Positive rate: values increase (line goes up 📈)
➖ Negative rate: values decrease (line goes down 📉)
🔹 Slope Connection 📐
The constant rate of change is also called the slope of a line.
🧮 Slope = change in y ÷ change in x
🔹 Key Words to Remember 📝
✅ Constant
✅ Same change
✅ Straight line
✅ Slope
✅ Steady speed
Learn with an example
📍 This graph shows how the amount of time that a receptionist named Colette spends on the phone is related to the number of phone calls she routes to employees.
What is the rate of change?
Write your answer as a decimal or integer.
______ minutes per phone call
Find any two points on the line.
Two points on the line are (0, 30) and (40, 60). Put those points into the slope formula.
slope = change in y / change in x
= 60 – 30 / 40 – 0 Plug in (0, 30) and (40, 60)
= 30 / 40 Subtract
= 3/4 Subtract
= 0.75 Write as a decimal
The slope is 0.75. The rate of change is 0.75 minutes per phone call.
📍 This graph shows how the number of cakes Donald can bake is related to the number of additional sticks of butter he buys.
What is the rate of change?
Write your answer as a decimal or integer.
_______ cakes per stick of butter
Find any two points on the line.
Two points on the line are (0, 3) and (1, 5). Put those points into the slope formula.
slope = change in y / change in x
= 5 – 3 / 1 – 0 Plug in (0, 3) and (1, 5)
= 2/1 Subtract
= 2 Subtract
The slope is 2. The rate of change is 2 cakes per stick of butter.
📍 This graph shows how the amount of time that a receptionist named Danny spends on the phone is related to the number of phone calls he routes to employees.
What is the rate of change?
Write your answer as a decimal or integer.
_________ minutes per phone call
Find any two points on the line.
Two points on the line are (0, 3) and (5, 4). Put those points into the slope formula.
slope = change in y / change in x
= 4 – 3 / 5 – 0 Plug in (0, 3) and (5, 4)
= 1/5 Subtract
= 0 . 2 Write as a decimal
The slope is 0.2. The rate of change is 0.20 minutes per phone call.
let’s practice! 🖊️
