1. 4-6 Graphing Linear Functions Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

2. Warm Up Interpret the graph. A rocket is fired into the air. The rocket’s speed increases until gravity gradually slows the rocket and causes it to fall to the ground. Course 2 4-6 Graphing Linear Functions Rocket Speed Time y x

3. Problem of the Day The mean of a, 31, 42, 65, and b is 51. The greatest number is 67 more than the least number. What are the missing numbers? 25 and 92 Course 2 4-6 Graphing Linear Functions

4. Learn to identify and graph linear equations. Course 2 4-6 Graphing Linear Functions

5. Vocabulary linear equation linear function Insert Lesson Title Here Course 2 4-6 Graphing Linear Functions

6. The graph at right shows how far an inner tube travels down a river if the current flows 2 miles per hour. The graph is linear because all the points fall on a line. It is part of the graph of a linear equation. 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 Course 2 4-6 Graphing Linear Functions

7. 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. Course 2 4-6 Graphing Linear Functions

8. Graph the linear function y = 4x - 1. Additional Example 1: Graphing Linear Functions 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) Course 2 4-6 Graphing Linear Functions

9. Additional Example 1 Continued 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) Course 2 4-6 Graphing Linear Functions

10. Graph the linear function y = 3x + 1. Input RuleOutput Ordered Pair x3x + 1y(x, y) 0 1 –1 3(0) + 1 3(1) + 1 3(–1) + 1 1 4 –2 (0, 1) (1, 4) (–1, –2) Check It Out: Example 1 Course 2 4-6 Graphing Linear Functions

11. Check It Out: Example 1 Continued Graph the linear function y = 3x + 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, 4) (–1, –2) Course 2 4-6 Graphing Linear Functions

12. The fastest-moving tectonic plates on Earth move apart at a rate of 15 centimeters per year. Scientists began studying two parts of these plates when they were 30 centimeters apart. Write a linear function that describes the movement of the plates over time. Then make a graph to show the movement over 4 years. Additional Example 2: Earth Science Application Begin by making a function table. Include a column for the rule. Course 2 4-6 Graphing Linear Functions

13. Additional Example 2 Continued InputRuleOutput 15(x) + 30 x 0 2 4 15(0) + 30 15(2) + 30 15(4) + 30 y 30 60 90 Let x represent the input and y represent the output. Course 2 4-6 Graphing Linear Functions Multiply the input by 15 and then add 30. The function is y = 15x + 30, where x is the number of years and y is the total centimeters apart the two plates are.

14. Additional Example 2 Continued Graph the ordered pairs (0, 30), (2, 60), and (4, 90) from your table. Connect the points with a line. x Course 2 4-6 Graphing Linear Functions Centimeters Years

15. Check It Out: Example 2 Insert Lesson Title Here 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. Course 2 4-6 Graphing Linear Functions Begin by making a function table. Include a column for the rule.

16. 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.

17. Check It Out: Example 2 Continued Insert Lesson Title Here x Course 2 4-6 Graphing Linear Functions Graph the ordered pairs (0, 21), (2, 35), and (4, 49) from your table. Connect the points with a line. Human Year Years

18. Lesson Quiz: Part I Graph the linear functions. 1. y = 3x – 4 2. y = –x + 4 3. y = 2 Insert Lesson Title Here y = 3x – 4 y = –x +4 y = 2 Course 2 4-6 Graphing Linear Functions

19. Lesson Quiz: Part II 4. The temperature of a liquid is decreasing at a rate of 12°F per hour. Susan begins measuring the liquid at 200°F. Write a linear function that describes the change in temperature over time. Then make a graph to show the temperature over 5 hours. y = 200 – 12x Insert Lesson Title Here Course 2 4-6 Graphing Linear Functions