Graphing Linear Functions and Special Cases

This page covers advanced concepts in graphing linear functions and special line cases.

Highlight: The process for graphing linear functions involves:

1. Determining slope and y-intercept
2. Plotting the y-intercept
3. Using slope to find another point
4. Connecting the points

Definition: Vertical lines are represented by x = a, while horizontal lines are represented by y = b.

Example: For the function y = x - 3, the slope is 1 and y-intercept is -3.

Vocabulary: Parallel lines have the same slope, while perpendicular lines have slopes that are opposite reciprocals.

Example: If one line has a slope of 3, its perpendicular line would have a slope of -1/3.

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.