Linear Functions Fundamentals and Real-World Applications

This page introduces the core concepts of linear functions and demonstrates their practical applications through various examples.

Definition: A linear function can be written as f(x) = mx + b, where m represents the slope and b is the y-intercept.

Highlight: The slope (m) indicates whether a function is increasing (m>0) or decreasing (m<0).

Example: In a population growth problem, a town's population was modeled using P(t) = 3000t + 48000, where t represents years after 2000.

Example: A phone company's pricing model is represented by C(m) = 10 + 0.05m, where m is the number of messages.

Vocabulary: Change in y (Δy) over change in x (Δx) remains constant for linear functions, defining their linear nature.