Rate of change

Learning Objectives Define 'rate of change' and explain its meaning in the context of a function. Calculate the rate of change from a table of values for a linear function. Determine the rate of change from a graph of a linear function. Calculate the rate of change given two points on a line. Interpret the meaning of the rate of change in real-world scenarios. Identify the rate of change (slope) in a linear equation written in slope-intercept form. Have you ever thought about how quickly things change around you? 📈 From the speed of a car to the growth of a plant, change is everywhere! In this lesson, you'll learn what 'rate of change' means in mathematics, especially when we talk about functions. Understanding rate of change helps us describe how...

TermDefinitionExample Rate of ChangeThe rate of change describes how one quantity changes in relation to another quantity. It's often expressed as a ratio comparing the change in the dependent variable to the change in the independent variable.If a car travels 60 miles in 2 hours, its rate of change (speed) is 30 miles per hour. SlopeFor linear functions, the rate of change is also known as the slope. It measures the steepness and direction of a line on a graph.A line that goes up from left to right has a positive slope, meaning a positive rate of change. Linear FunctionA function whose graph is a straight line. Linear functions have a constant rate of change, meaning the rate of change never varies.The equation y = 2x + 3 represents a linear function because its graph is a straight...

Rate of Change Formula (Slope Formula) $$m = \frac{\text{Change in y}}{\text{Change in x}} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}$$ This formula is used to calculate the rate of change (or slope) between any two distinct points $(x_1, y_1)$ and $(x_2, y_2)$ on a line or in a data set. The 'm' typically represents the slope. Slope-Intercept Form of a Linear Equation $$y = mx + b$$ This is a common way to write the equation of a linear function. In this form, 'm' directly represents the rate of change (slope) of the line, and 'b' represents the y-intercept (where the line crosses the y-axis).