Interpret linear functions

Learning Objectives Identify the slope and y-intercept of a linear function from equations, graphs, and tables. Explain the meaning of the slope as a rate of change in real-world contexts. Explain the meaning of the y-intercept as an initial value or starting point in real-world contexts. Relate the independent and dependent variables to the context of a linear function. Use interpretations of slope and y-intercept to answer questions about real-world scenarios. Compare and contrast different linear functions based on their contextual interpretations. Ever wonder how scientists predict the path of a hurricane or how much money you'll save over time? 🌀 Linear functions help us understand these patterns! In this lesson, you'll learn how to 'read between the li...

TermDefinitionExample Linear FunctionA relationship between two variables that, when graphed, forms a straight line. It describes a constant rate of change.The relationship between the number of hours worked and the money earned, if you get paid a fixed amount per hour. Slope (m)The measure of the steepness of a line, representing the rate of change of the dependent variable with respect to the independent variable. It's often described as 'rise over run'.If a car travels at 60 miles per hour, the slope is 60 miles/hour, meaning for every 1 hour, the distance increases by 60 miles. Y-intercept (b)The point where the line crosses the y-axis. It represents the value of the dependent variable when the independent variable is zero.In a savings account, the initial deposit is th...

Slope Formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ Used to calculate the slope (rate of change) of a line given any two points $(x_1, y_1)$ and $(x_2, y_2)$ on the line. Slope-Intercept Form $y = mx + b$ A common way to write linear equations, where 'm' is the slope and 'b' is the y-intercept. This form makes it easy to identify these key features. Interpreting Slope in Context For every 1 unit increase in the independent variable (x), the dependent variable (y) changes by 'm' units. This rule helps translate the numerical value of the slope into a meaningful statement about the relationship between the quantities in a real-world problem, including units. Interpreting Y-intercept in Context When the independent variable (x) is 0, the...