Constant rate of change

Learning Objectives Define rate of change and identify situations where it is constant. Calculate the constant rate of change from a table of values using integer operations. Determine the constant rate of change from a graph of a linear relationship. Interpret the meaning of a constant rate of change in real-world contexts. Distinguish between constant and non-constant rates of change. Apply the concept of constant rate of change to predict future values in a linear pattern. Ever wonder how fast a car is traveling or how quickly your savings grow? 🚗💰 In this lesson, you'll learn about the 'constant rate of change,' a fundamental concept that helps us understand how quantities change predictably over time or in relation to other quantities. This is crucial...

TermDefinitionExample RateA ratio comparing two quantities with different units.60 miles per 2 hours, or $15 per hour. ChangeThe difference between a final value and an initial value. It can be positive (increase) or negative (decrease).If a temperature goes from 5°C to 10°C, the change is 10 - 5 = 5°C. If it goes from 10°C to 5°C, the change is 5 - 10 = -5°C. Rate of ChangeHow one quantity changes in relation to another quantity. It's often expressed as a ratio of the change in the dependent variable to the change in the independent variable.A plant grows 2 cm per week. The rate of change is 2 cm/week. Constant Rate of ChangeWhen the rate of change between any two points in a relationship remains the same. This indicates a linear relationship.A car travels 50 miles every hour. The r...

Formula for Rate of Change (Slope) $m = \frac{\text{change in dependent variable}}{\text{change in independent variable}} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}$ This formula is used to calculate the constant rate of change (slope) between any two points $(x_1, y_1)$ and $(x_2, y_2)$ in a linear relationship. $\Delta$ (delta) means 'change in'. Identifying Constant Rate of Change from a Table A relationship has a constant rate of change if the ratio of the change in the dependent variable (y) to the change in the independent variable (x) is the same for all consecutive pairs of data points. To use this, calculate $\frac{\Delta y}{\Delta x}$ for several pairs of points in a table. If the result is always the same, the rate of change is constant, i...