2. A4.c How Do I Graph Equations Of The Form y = mx + b ? Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

3. 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 Course 3 A4.c How Do I Graph Equations Of The Form y = mx + b ? y = – 2x + 6 y = x + 8 5 2

4. 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 Course 3 A4.c How Do I Graph Equations Of The Form y = mx + b ?

5. Learn to identify and graph linear equations. Course 3 A4.c How Do I Graph Equations Of The Form y = mx + b ?

6. Vocabulary Linear equation Insert Lesson Title Here Course 3 A4.c How Do I Graph Equations Of The Form y = mx + b ?

7. 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. Course 3 A4.c How Do I Graph Equations Of The Form y = mx + b ?

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 Course 3 A4.c How Do I Graph Equations Of The Form y = mx + b ?

9. Graph the equation and tell whether it is linear. y = 3x – 1 Example 1A: Graphing Equations 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) Course 3 A4.c How Do I Graph Equations Of The Form y = mx + b ?

10. 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. Course 3 A4.c How Do I Graph Equations Of The Form y = mx + b ?

11. Insert Lesson Title Here Be careful when graphing each ordered pair. Double check each point you plot. Caution! Course 3 A4.c How Do I Graph Equations Of The Form y = mx + b ?

12. Graph the equation and tell whether it is linear. y = 2x + 1 Check it Out: Example 1A x2x + 1y(x, y) –4 –2 0 2 4 –72(–4) + 1 2(–2) + 1 2(0) + 1 2(2) + 1 2(4) + 1 –3 1 5 9 (–4, –7) (–2, –3) (0, 1) (2, 5) (4, 9) Course 3 A4.c How Do I Graph Equations Of The Form y = mx + b ?

13. Check It Out: Example 1A Continued The equation y = 2x + 1 is linear equation because it is the graph of a straight line and each time x increases by 1 unit, y increases by 2 units. Course 3 A4.c How Do I Graph Equations Of The Form y = mx + b ?

14. Graph the equation and tell whether it is linear. y = x 3 Example 1B: Graphing Equations 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) Course 3 A4.c How Do I Graph Equations Of The Form y = mx + b ?

15. Example 1B 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 Course 3 A4.c How Do I Graph Equations Of The Form y = mx + b ?

16. Graphing the equation and tell whether it is linear. y = x 2 Check It Out: Example 1B 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 Course 3 A4.c How Do I Graph Equations Of The Form y = mx + b ?

17. Check It Out: Example 1B Continued The equation y = x 2 is not a linear equation because its graph is not a straight line. It is called nonlinear. Course 3 A4.c How Do I Graph Equations Of The Form y = mx + b ?

18. Example 1C: Graphing Equations Graph the equation and tell whether it is linear. y = – 3x3x 4 Course 3 A4.c How Do I Graph Equations Of The Form y = mx + b ?

19. Example 1C 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 Course 3 A4.c How Do I Graph Equations Of The Form y = mx + b ?

20. Check It Out: Example 1C Graph the equation and tell whether it is linear. 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) Course 3 A4.c How Do I Graph Equations Of The Form y = mx + b ?

21. Check It Out: Example 1C 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. Course 3 A4.c How Do I Graph Equations Of The Form y = mx + b ?

22. Graph the equation and tell whether it is linear. y = 2 Example 1D: Graphing Equations 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) Course 3 A4.c How Do I Graph Equations Of The Form y = mx + b ?

23. Example 1D 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 (the value of y stays the same). Course 3 A4.c How Do I Graph Equations Of The Form y = mx + b ?

24. Check It Out: Example 1D 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) Course 3 A4.c How Do I Graph Equations Of The Form y = mx + b ?

25. Check It Out: Example 1D 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. Course 3 A4.c How Do I Graph Equations Of The Form y = mx + b ?

26. Example 2: 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. Course 3 A4.c How Do I Graph Equations Of The Form y = mx + b ?

27. Example 2 Continued Course 3 A4.c How Do I Graph Equations Of The Form y = mx + b ?

28. Example 2 Continued Course 3 A4.c How Do I Graph Equations Of The Form y = mx + b ?

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. Example 2 Continued Course 3 A4.c How Do I Graph Equations Of The Form y = mx + b ?

30. Check It Out: Example 2 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 Course 3 A4.c How Do I Graph Equations Of The Form y = mx + b ?

31. Check It Out: Example 2 Continued tD =1250tD(t, D) 11250(1)1250(1, 1250) 21250(2)2500(2, 2500) 31250(3)3750(3, 3750) Course 3 A4.c How Do I Graph Equations Of The Form y = mx + b ? The distances are: Ryan, 1250 ft; Greg, 2500 ft; and Collette, 3750 ft.

32. Check It Out: Example 2 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) Course 3 A4.c How Do I Graph Equations Of The Form y = mx + b ?

33. Lesson Quiz Graph each equation and tell whether it is linear. 1. y = 3x – 1 2. y = x 3. y = x 2 – 3 yes Insert Lesson Title Here no 1414 Course 3 A4.c How Do I Graph Equations Of The Form y = mx + b ?