Interpret the equation y = mx + b as defining a linear function

What you'll learn

1. Explain why the equation y = mx + b defines a function by identifying the input (x), the output (y), and the rule (multiply by m, then add b) that assigns exactly one output to each input
2. Identify a linear function by verifying that the rate of change between consecutive entries in a table is constant (equal differences in y for equal differences in x)
3. Explain why the graph of y = mx + b is a straight line and connect the constant rate of change to the straightness of the graph
4. Give examples of functions that are not linear by constructing tables and graphs for rules such as y = x^2, y = 1/x, or y = 2^x, and showing that the rate of change is not constant
5. Classify a function as linear or nonlinear given its equation, table, or graph, and justify the classification using the constant-rate-of-change criterion

Prerequisites

• Understand that a function is a rule that assigns to each input exactly one output
• Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line