Section 2-2 Linear Equations Objective: To graph a relation, state its domain and range, and determine if it is a function. To find values of functions for given elements of the domain. Algebra II

Independent vs. Dependent Independent Variable – usually graphed on the horizontal or x-axis Dependent Variable – usually graphed on the vertical or y-axis The speed of sound through air. Algebra II

Speed of Sound Graph

Standard Form of a Linear Equation Ax + By = C Algebra II

Example 1a Write this equation in standard form where A, B, and C are integers whose greatest common factor is 1. Identify A, B, and C. y = -5x + 6 Algebra II

Example 1b Write this equation in standard form where A, B, and C are integers whose greatest common factor is 1. Identify A, B, and C. Algebra II

Example 1c Write this equation in standard form where A, B, and C are integers whose greatest common factor is 1. Identify A, B, and C. 5x – 10y = 25 Algebra II

Definition of a Linear Function Algebra II

Example 2 State whether each function is a linear function. a. f(x) = 4x + 5 b. f(x) = x3 + 2 c. f(x) = 9 – 6x Algebra II

Intercepts Graphing Method The x-intercept is the point at which the graph crosses the x-axis. The y-intercept is the point at which the graph crosses the y-axis. Algebra II

Example 3 Graph 5x – 3y = 15 using the x- and y-intercepts. The x-intercept is the value of x when y is 0. The y-intercept is the value of y when x is 0. ( , 0) (0, ) 5x – 3y = 15 Algebra II

Example 3 cont. ( , 0) (0, ) 5x – 3y = 15

Homework 2-2 pg 77 #18-45 by 3’s Algebra II