1. Graphing Linear Equations 8-1 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

2. Graphing Linear Equations 8-1 Warm Up Solve each equation for y. 1. 6y – 12x = 24 2. – 2y – 4x = 20 3. 2y – 5x = 16 4. 3y + 6x = 18 y = 2x + 4 y = – 2x – 10 y = – 2x + 6 y = x + 8 5 2

3. Graphing Linear Equations 8-1 Problem of the Day The same photo book of Niagara Falls costs $5.95 in the United States and $8.25 in Canada. If the exchange rate is $1.49 in Canadian dollars for each U.S. dollar, in which country is the book a better deal? Canada

4. Graphing Linear Equations 8-1 MA.8.A.1.6 Compare the graphs of linear and non-linear functions for real-world situations. Also MA.8.A.1.1, MA.8.A.1.5 Sunshine State Standards

5. Graphing Linear Equations 8-1 Vocabulary linear equation rate of change

6. Graphing Linear Equations 8-1 A linear equation is an equation whose solutions fall on a line on the coordinate plane. All solutions of a particular linear equation fall on the line, and all the points on the line are solutions of the equation.

7. Graphing Linear Equations 8-1 If an equation is linear, a constant change in the x-value corresponds to a constant change in the y-value. The graph shows an example where each time the x-value increases by 3, the y-value increases by 2.

8. Graphing Linear Equations 8-1 Graph the equation and tell whether it is linear. y = 3x – 1 Additional Example 1A: Graphing Equations x–1012 y–4–4–1–125 +3 Make a table of ordered pairs. Find the differences between consecutive data points. +1

9. Graphing Linear Equations 8-1 Additional Example 1A Continued The equation y = 3x – 1 is a linear equation because it is the graph of a straight line and each time x increases by 1 unit, y increases by 3 units.

10. Graphing Linear Equations 8-1 Be careful when graphing each ordered pair. Double check each point you plot. Caution!

11. Graphing Linear Equations 8-1 Additional Example 1B: Graphing Equations Graph the equation and tell whether it is linear. y = 2 The equation y = 2 is a linear equation because it is the graph of the horizontal line where every y-coordinate is 2.

12. Graphing Linear Equations 8-1 Graph each equation and tell whether it is linear. y = 2x + 1 Check It Out: Example 1A x–2–2–1–1012 y–3–3–1–1135 linear

13. Graphing Linear Equations 8-1 Check It Out: Example 1A Continued

14. Graphing Linear Equations 8-1 Graph each equation and tell whether it is linear. y = x 2 + 1 Check It Out: Example 1B x–2–2–1–1012 y 5 2125 non linear

15. Graphing Linear Equations 8-1 Check It Out: Example 1B Continued

16. Graphing Linear Equations 8-1 A rate of change is a ratio that compares the amount of change in a dependent variable to the amount of change in an independent variable. The rates for a set of data may vary, or they may be constant.

17. Graphing Linear Equations 8-1 Determine whether the rates of change are constant or variable. Additional Example 2A: Identifying Constant and Variable Rates of Change in Data Find the difference between consecutive data points. x01358 y0261016 +1 +2 +3 +2+4 +6 Find each ratio of change in y to change in x. 2121 = 2 4242 4242 6363 The rates of change are constant.

18. Graphing Linear Equations 8-1 Determine whether the rates of change are constant or variable. Additional Example 2B: Identifying Constant and Variable Rates of Change in Data Find the difference between consecutive data points. x13469 y02663 +2 +1 +2+3 +2+4+0+3 Find each ratio of change in y to change in x.2 = 1 4141 = 4 0202 = 03 = 1 The rates of change are variable.

19. Graphing Linear Equations 8-1 Determine whether the rates of change are constant or variable. Check It Out: Example 2A x01234 y13579 The rates of change are constant.

20. Graphing Linear Equations 8-1 Determine whether the rates of change are constant or variable. Check It Out: Example 2B x–2–2–1–1012 y0–3–3–4–4–3–30 The rates of change are variable.

21. Graphing Linear Equations 8-1 Additional Example 3: Sports Application A lift on a ski slope rises according to the equation a = 130t + 6250, where a is the altitude in feet and t is the number of minutes that a skier has been on the lift. Five friends are on the lift. What is the altitude of each person if they have been on the ski lift for the times listed in the table? Draw a graph that represents the relationship between the time on the lift and the altitude.

22. Graphing Linear Equations 8-1 Additional Example 3 Continued

23. Graphing Linear Equations 8-1 Additional Example 3 Continued

24. Graphing Linear Equations 8-1 The altitudes are: Anna, 6770 feet; Tracy, 6640 feet; Kwani, 6510 feet; Tony, 6445 feet; George, 6380 feet. This is a linear equation because when t increases by 1 unit, a increases by 130 units. Note that a skier with 0 time on the lift implies that the bottom of the lift is at an altitude of 6250 feet. Additional Example 3 Continued

25. Graphing Linear Equations 8-1 Check It Out: Example 3 A home improvement store charges a base fee of $150, plus $25 for each hour of machinery rental. The cost C for h hours is given by C = 25h + 150. Find the cost for 1, 2, 3, 4, and 5 hours. Is this a linear equation? Draw a graph that represents the relationship between the cost and the number of hours of rental. 1 hr = $175, 2 hr = $200, 3 hr = $225 4 hr = $250, 5 hr = $275; linear

26. Graphing Linear Equations 8-1 Check It Out: Example 3 Continued

27. Graphing Linear Equations 8-1 Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

28. Graphing Linear Equations 8-1 Lesson Quiz Graph each equation and tell whether it is linear. 1. y = 3x – 1 2. y = x 3. y = x 2 – 3 yes no 1414

29. Graphing Linear Equations 8-1 1. Identify the graph of the equation y = 4x – 1 and tell whether it is linear. A. yesB. yes Lesson Quiz for Student Response Systems

30. Graphing Linear Equations 8-1 2. Identify the graph of the equation and tell whether it is linear. A. yesB. yes Lesson Quiz for Student Response Systems

31. Graphing Linear Equations 8-1 3. Identify the graph of the equation y = x 2 – 9 and tell whether it is linear. A. noB. no Lesson Quiz for Student Response Systems