Linear vs Nonlinear Data Analysis

This page presents a detailed comparison between linear and nonlinear data patterns, essential for understanding graphing linear equations in two variables.

Definition: Linear data exhibits a constant rate of change and produces a straight line when graphed, while nonlinear data shows varying rates of change and creates curved lines.

Example: In a linear pattern, if x increases by 2, y consistently increases by 3, demonstrating a constant rate of change linear function. In contrast, a non linear function example might show y increasing by larger amounts (2, 4, 6) as x increases uniformly.

Highlight: The equation y = 3x² represents a nonlinear relationship, demonstrating exponential growth.

Vocabulary: Rate of change refers to how much y changes in relation to changes in x. In linear functions, this rate remains constant, while in nonlinear table examples, it varies.

Understanding Slope and Y-intercept

This page introduces fundamental concepts of linear equations and their graphical representations. The slope $m$ represents the steepness of a line and can be calculated through multiple methods.

Definition: Y-intercept is the point where a linear graph crosses the y-axis, representing the value of y when x equals 0 (denoted as b).

Example: Using two points (4,1) and (7,5), the slope can be calculated as m = $5-1$/$7-4$ = 4/3.

Highlight: Slopes can be categorized into different types:

• Positive slope (rising line)
• Negative slope (falling line)
• Zero slope (horizontal line)
• Undefined slope (vertical line)

Vocabulary: The slope formula using two points is expressed as m = $y₂-y₁$/$x₂-x₁$, where (x₁,y₁) and (x₂,y₂) are coordinates of two points on the line.