1. Objective: to identify and graph linear equations. Chapter 7-3 Standards AF 3.3 & AF 1.1

2. Vocabulary linear equation linear function

3. A linear equation is an equation whose graph is a line. The solutions of a linear equation are the points that make up its graph. Linear equations and linear graphs can be different representations of linear functions. A linear function is a function whose graph is a nonvertical line. y 0 24 2 4 6 x Miles Hours 0

4. Only two points are needed to draw the graph of a linear function. However, graphing a third point serves as a check. You can use a function table to find each ordered pair.

5. Graph the linear function y = 4x - 1. Input RuleOutput Ordered Pair x4x – 1y(x, y) 0 1 –1 4(0) – 1 4(1) – 1 4(–1) – 1 –1 3 –5 (0, –1) (1, 3) (–1, –5)

6. Graph the linear function y = 4x - 1. Place each ordered pair on the coordinate grid and then connect the points with a line. x y 0 –2 –4 24 2 4 –2 –4 (0, –1) (1, 3) (–1, –5)

7. Graph the linear function y = 3x + 1.

8. Place each ordered pair on the coordinate grid and then connect the points with a line. x y 0 –2 –4 24 2 4 –2 –4 (0, 1) (1, 4) (–1, –2)

9. Dogs are considered to age 7 years for each human year. If a dog is 3 years old today, how old in human years will it be in 4 more years? Write a linear equation which would show this relationship. Then make a graph to show how the dog will age in human years over the next 4 years. Begin by making a function table. Include a column for the rule.

10. Check It Out: Example 2 Continued Insert Lesson Title Here InputRuleOutput 7(x) + 21 x 0 2 4 7(0) + 21 7(2) + 21 7(4) + 21 y 21 35 49 Course 2 4-6 Graphing Linear Functions Let x represent the input and y represent the output. Multiply the input by 7 and then add 21. The function is y = 7x + 21, where x is the number of years and y is the total age of the dog in human years.

11. x Graph the ordered pairs (0, 21), (2, 35), and (4, 49) from your table. Connect the points with a line. Human Year Years

12. Lesson Quiz Graph the linear functions. 1. y = 3x – 4 2. y = –x + 4 3. y = 2 y = 3x – 4 y = –x +4 y = 2