Constant rate of change

Learning Objectives Define constant rate of change and identify its components. Calculate constant rates of change from given data, including decimal values. Interpret the meaning of a constant rate of change in real-world scenarios. Distinguish between constant and non-constant rates of change. Use constant rates of change to make predictions involving decimal quantities. Express constant rates of change as unit rates with appropriate units. Analyze tables and simple graphs to determine if a constant rate of change exists. Have you ever noticed how some things change at a steady, predictable pace, like a car traveling at the same speed? 🚗 In this lesson, you'll learn about the 'constant rate of change,' which helps us understand how one quantity changes i...

TermDefinitionExample RateA ratio that compares two quantities measured in different units.If a car travels 60 miles in 2 hours, the rate is 30 miles per hour. Constant Rate of ChangeA rate where the relationship between two quantities remains the same over any interval. This means the change in one quantity divided by the change in the other quantity is always the same value.If a baker uses 0.5 cups of flour for every 1 cake, and 1 cup for every 2 cakes, the constant rate of change is 0.5 cups per cake. Unit RateA rate where the second quantity in the comparison is 1 unit. It simplifies the rate to show 'how much per one'.If you earn $15.75 for 3 hours of work, the unit rate is $5.25 per hour. Independent VariableThe quantity that changes freely or is controlled, and whose chan...

Formula for Rate of Change $$\text{Rate of Change} = \frac{\text{Change in Dependent Variable}}{\text{Change in Independent Variable}}$$ This formula is used to calculate how much one quantity changes for every unit change in another quantity. For a constant rate, this value will be the same across all intervals. Calculating Unit Rate $$\text{Unit Rate} = \frac{\text{Total Quantity of Dependent Variable}}{\text{Total Quantity of Independent Variable}}$$ To find the unit rate, divide the total amount of the dependent variable by the total amount of the independent variable. This gives you 'how much per 1 unit' of the independent variable. Proportionality Test (for Constant Rate) $$\frac{y}{x} = k \quad \text{or} \quad \frac{\text{Dependent Variable}}{\text{Ind...