1. Pre-Algebra 11-1 Graphing Linear Equations 11-1 Graphing Linear Equations Pre-Algebra Homework & Learning Goal Homework & Learning Goal Lesson Presentation Lesson Presentation

2. Pre-Algebra 11-1 Graphing Linear Equations Pre-Algebra HOMEWORK Page 543 #1-11

3. Pre-Algebra 11-1 Graphing Linear Equations Our Learning Goal Students will be able to graph lines using linear equations, understand the slope of a line and graph inequalities.

4. Pre-Algebra 11-1 Graphing Linear Equations Our Learning Goal Assignments Learn to identify and graph linear equations. Learn to find the slope of a line and use slope to understand and draw graphs. Learn to use slopes and intercepts to graph linear equations. Learn to find the equation of a line given one point and the slope. Learn to recognize direct variation by graphing tables of data and checking for constant ratios. Learn to graph inequalities on the coordinate plane. Learn to recognize relationships in data and find the equation of a line of best fit.

5. Pre-Algebra 11-1 Graphing Linear Equations Today’s Learning Goal Assignment Learn to identify and graph linear equations.

6. Pre-Algebra 11-1 Graphing Linear Equations 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 Pre-Algebra 11-1 Graphing Linear Equations y = -2x + 6 y = x + 8 5 2

7. Pre-Algebra 11-1 Graphing Linear Equations 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

8. Pre-Algebra 11-1 Graphing Linear Equations Learn to identify and graph linear equations.

9. Pre-Algebra 11-1 Graphing Linear Equations Vocabulary linear equation

10. Pre-Algebra 11-1 Graphing Linear Equations 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.

11. Pre-Algebra 11-1 Graphing Linear Equations Read x 1 as “x sub one” or “x one.” Reading Math

12. Pre-Algebra 11-1 Graphing Linear Equations 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

13. Pre-Algebra 11-1 Graphing Linear Equations Graph the equation and tell whether it is linear. A. y = 3x – 1 Additional 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)

14. Pre-Algebra 11-1 Graphing Linear Equations 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.

15. Pre-Algebra 11-1 Graphing Linear Equations Graph the equation and tell whether it is linear. B. y = x 3 Additional 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)

16. Pre-Algebra 11-1 Graphing Linear Equations Additional 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

17. Pre-Algebra 11-1 Graphing Linear Equations Additional Example 1C: Graphing Equations Graph the equation and tell whether it is linear. C. y = – 3x3x 4

18. Pre-Algebra 11-1 Graphing Linear Equations Additional Example 1 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

19. Pre-Algebra 11-1 Graphing Linear Equations Graph the equation and tell whether it is linear. D. y = 2 Additional 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)

20. Pre-Algebra 11-1 Graphing Linear Equations Additional 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.

21. Pre-Algebra 11-1 Graphing Linear Equations Graph the equation and tell whether it is linear. A. y = 2x + 1 Try This: Example 1A 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)

22. Pre-Algebra 11-1 Graphing Linear Equations Try This: Example 1A 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.

23. Pre-Algebra 11-1 Graphing Linear Equations Graphing the equation and tell whether it is linear. B. y = x 2 Try This: 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

24. Pre-Algebra 11-1 Graphing Linear Equations Try This: Example 1B Continued The equation y = x 2 is not a linear equation because its graph is not a straight line.

25. Pre-Algebra 11-1 Graphing Linear Equations Try This: Example 1C 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)

26. Pre-Algebra 11-1 Graphing Linear Equations Try This: 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.

27. Pre-Algebra 11-1 Graphing Linear Equations Try This: 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)

28. Pre-Algebra 11-1 Graphing Linear Equations Try This: 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.

29. Pre-Algebra 11-1 Graphing Linear Equations Additional 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.

30. Pre-Algebra 11-1 Graphing Linear Equations Additional Example 2 Continued

31. Pre-Algebra 11-1 Graphing Linear Equations Additional Example 2 Continued

32. Pre-Algebra 11-1 Graphing Linear Equations 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 2 Continued

33. Pre-Algebra 11-1 Graphing Linear Equations Try This: 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

34. Pre-Algebra 11-1 Graphing Linear Equations Try This: Example 2 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.

35. Pre-Algebra 11-1 Graphing Linear Equations Try This: 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)

36. Pre-Algebra 11-1 Graphing Linear Equations 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