2. 11-1 Graphing Linear Equations Pre-Algebra Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

3. Can You Solve This Real Life Problem? 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 and why is that? Prove it! Canada

4. 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

5. Learn to identify and graph linear equations. A continuation of what you began earlier….

6. 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. To find a solution that lies between two points (x 1, y 1 ) and (x 2, y 2 ), choose an x-value between x 1 and x 2 and find the corresponding y-value.

7. Read x 1 as “x sub one” or “x one.” Reading Math

8. 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. 3 3 3 2 2 2

9. Graph the equation and tell whether it is linear. A. y = 3x – 1 Try this and raise your hand when you are finished! x3x – 1y(x, y) –2 –1 0 1 2 –73(–2) – 1 3(–1) – 1 3(0) – 1 3(1) – 1 3(2) – 1 –4 –1 2 5 (–2, –7) (–1, –4) (0, –1) (1, 2) (2, 5)

10. 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.

11. Graph the equation and tell whether it is linear. B. y = x 3 Try Another! xx3x3 y(x, y) –2 –1 0 1 2 –8(–2) 3 (–1) 3 (0) 3 (1) 3 (2) 3 –1 0 1 8 (–2, –8) (–1, –1) (0, 0) (1, 1) (2, 8)

12. Continued The equation y = x 3 is not a linear equation because its graph is not a straight line. Also notice that as x increases by a constant of 1 unit, the change in y is not constant. x–2–2–1–1012 y–8–8–1–1018 +7+1 +7

13. How about this big guy? Graph the equation and tell whether it is linear. C. y = – 3x3x 4

14. How about this big guy? Graph the equation and tell whether it is linear. C. y = – 3x3x 4

15. Big Guy….Continued The equation y = – is a linear equation because the points form a straight line. Each time the value of x increases by 1, the value of y decreases by or y decreases by 3 each time x increases by 4. 3x3x 4 3 4

16. Graph the equation and tell whether it is linear. D. y = 2 Again…. For any value of x, y = 2. x2y(x, y) –2 –1 0 1 2 22 2 2 2 2 2 2 2 2 (–2, 2) (–1, 2) (0, 2) (1, 2) (2, 2)

17. Continued The equation y = 2 is a linear equation because the points form a straight line. As the value of x increases, the value of y has a constant change of 0.

18. Graph the equation and tell whether it is linear. A. y = 2x + 1 Try This: x2x + 1y(x, y) –2 –1 0 1 2 –32(–2) + 1 2(–1) + 1 2(0) + 1 2(1) + 1 2(2) + 1 –1 1 3 5 (–3, –3) (–2, –1) (–1, 1) (0, 3) (2, 5)

19. Continued The equation y = 2x + 1 is linear equation because it is the graph of a straight line and each time x increase by 1 unit, y increases by 2 units.

20. Graphing the equation and tell whether it is linear. B. y = x 2 Try This: xx2x2 y(x, y) –2 –1 0 1 2 4(–2) 2 1 0 1 4 (–2, 4) (–1, 1) (0, 0) (1, 1) (2, 4) (–1) 2 (0) 2 (1) 2 (2) 2

21. Continued The equation y = x 2 is not a linear equation because its graph is not a straight line.

22. Try This: Graph the equation and tell whether it is linear. C. y = x xy(x, y) –8 –6 0 4 8 –8 –6 0 4 8 (–8, –8) (–6, –6) (0, 0) (4, 4) (8, 8)

23. Continued The equation y = x is a linear equation because the points form a straight line. Each time the value of x increases by 1, the value of y increases by 1.

24. Try one more before we go on to real life! For any value of x, y = 7. Graph the equation and tell whether it is linear. D. y = 7 x7y(x, y) –8 –4 0 4 8 77 7 7 7 7 7 7 7 7 (–8, 7) (–4, 7) (0, 7) (4, 7) (8, 7)

25. Continued The equation y = 7 is a linear equation because the points form a straight line. As the value of x increases, the value of y has a constant change of 0.

26. 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.

27. Here is how I answered it!

28. Additional Example 2 Continued

29. 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. Continued

30. Let’s try another one in teams! In an amusement park ride, a car travels according to the equation D = 1250t where t is time in minutes and D is the distance in feet the car travels. Below is a chart of the time that three people have been in the cars. Graph the relationship between time and distance. How far has each person traveled? RiderTime Ryan1 min Greg2 min Colette3 min

31. Continued tD =1250tD(t, D) 11250(1)1250(1, 1250) 21250(2)2500(2, 2500) 31250(3)3750(3, 3750) The distances are: Ryan, 1250 ft; Greg, 2500 ft; and Collette, 3750 ft.

32. Continued x y This is a linear equation because when t increases by 1 unit, D increases by 1250 units. 1250 2500 12 3750 5000 34 Time (min) Distance (ft)

33. Let’s See What You leaned… Graph each equation and tell whether it is linear. 1. y = 3x – 1 2. y = x 3. y = x 2 – 3 yes no 1414 I mean “learned”

34. Today’s Assignment Write it in your planner, now!