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

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8.F.A.3

**8.F.A.3**: Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s^2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.

8.F.A.3: Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s^2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.

What you'll learn

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
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)
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
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
Classify a function as linear or nonlinear given its equation, table, or graph, and justify the classification using the constant-rate-of-change criterion

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Linear and nonlinear functions

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