1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

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

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

4. Learn to identify and graph linear equations.

5. Vocabulary
linear equation
linear function

6. y 2 4 6 x
Miles
Hours
The graph at right shows how far a kayak 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.

7. Only two points are needed to draw the graph of a linear function
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.

8. Additional Example 1: Graphing Linear Functions
Graph the linear function y = 4x - 1.
Input
Rule
Output
Ordered Pair x
4x – 1 y
(x, y)‏
4(0) – 1 –1
(0, –1)‏ 1
4(1) – 1 3
(1, 3)‏ –1
4(–1) – 1 –5
(–1, –5)‏

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

10. Graph the linear function y = 3x + 1.
Check It Out: Example 1
Graph the linear function y = 3x + 1.
Input
Rule
Output
Ordered Pair x
3x + 1 y
(x, y)‏
3(0) + 1 1
(0, 1)‏ 1
3(1) + 1 4
(1, 4)‏ –1
3(–1) + 1 –2
(–1, –2)‏

11. Check It Out: Example 1 Continued
Graph the linear function y = 3x + 1. x y
(1, 4)‏ 4
Place each ordered pair on the coordinate grid and then connect the points with a line. 2
(0, 1)‏ –4 –2 2 4 –2
(–1, –2)‏ –4

12. Additional Example 2: Earth Science Application
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.
Begin by making a function table. Include a column for the rule.

13. Additional Example 2 Continued
Output
Rule
Input x
15(x) + 30 y
Multiply the input by 15 and then add 30.
15(0) + 30 30 2
15(2) + 30 60 4
15(4) + 30 90
Let x represent the input and y represent the output.
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. y
100 80 60 40 20 2 4 8 10 12
Check
Substitute the ordered
pairs into th function
y = 15x + 30.
Centimeters
30 = 15(0) + 30 ​?
30 = 30 ? x
90 = 15(4) + 30 ​?
Years
90 = 90 ?

15. Check It Out: Example 2
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.

16. Check It Out: Example 2 Continued
Output
Rule
Input x
7(x) + 21 y
Multiply the input by 7 and then add 21.
7(0) + 21 21 2
7(2) + 21 35 4
7(4) + 21 49
Let x represent the input and y represent the output.
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
Graph the ordered pairs (0, 21), (2, 35), and (4, 49) from your table. Connect the points with a line. y 80 60 40 20 2 4 8 10
Check
Substitute the ordered
pairs into th function
y = 15x + 30.
Human Year
30 = 15(0) + 30 ​?
30 = 30 ? x
90 = 15(4) + 30 ​?
Years
90 = 90 ?

18. Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems

19. Graph the linear functions. 1. y = 3x – 4 2. y = –x + 4 3. y = 2
Lesson Quiz: Part I
Graph the linear functions.
1. y = 3x – 4
2. y = –x + 4
3. y = 2
y = –x +4
y = 2
y = 3x – 4

20. 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

21. Lesson Quiz for Student Response Systems
1. Identify the graph of the linear function y = 2x – 5.
A B.

22. Lesson Quiz for Student Response Systems
2. Identify the graph of the linear function y = –x + 4.
A B.

23. Lesson Quiz for Student Response Systems
3. Identify the graph of the linear function y = 5.
A B.

24. Lesson Quiz for Student Response Systems
4. Larry has 150 cents in his piggy bank. He puts 20 cents into it everyday. Identify a linear function that describes the amount in the piggy bank over time and a graph that shows the amount over 5 days.
A. y = 150 – 20x B. y = x