2.4 Graphs of Linear Functions
Objective 1: Graph Linear Functions by Plotting Points
Example: List 5 pairs of numbers that add to 10. For each pair, call one number x and the other
number y.
Plot these points on a set of coordinate axes. Connect the dots.
How many pairs of numbers add to 10? ______________
What shape is the graph? ________________
What does the graph represent? _________________
Definition
Linear Equation in Two Variables (Standard Form)
A linear equation in two variables is an equation that can be written in the standard form
, where A, B, and C are real numbers, and A and B are not both equal to 0.
Definition
Linear Function
A linear function is a function of the form f (x) = ax + b , where a and b are real numbers.
To graph a linear function by plotting points
1. Solve the equation for y.
2. Find three ordered pairs by picking values for x and solving for y. (x, y)
3. Plot the points. Connect the points.
How many points determine a line?
Why do we pick 3 points?
2.4.2 Graph the function by plotting points.
Objective 2: Graph Linear Functions by Using Intercepts
Finding - and -Intercepts of a Graph Given an Equation
 To find an -intercept, let
 To find a -intercept, let
(or
and solve for
) and solve for .
(or evaluate
).
NOTE: This method of finding intercepts is used for graphing of all functions and relations.
2.4.12 Graph the function by using intercepts.
Objective 3: Graph Vertical and Horizontal Lines
A Horizontal line has equation ________________________
A Vertical line has equation
________________________
Examples:
Give an example of the equation of a horizontal line and graph it.
Give an example of the equation of a vertical line and graph it.