1. Lines Chapter 1.1

2. Increments 2

3. Example 1: Finding Increments 3

4. 4

5. Slope of a Line 5

6. 6

7. 7

8. Positive Slope of a Line 8

9. Negative Slope of a Line 9

10. Theorems and Definitions As we continue in the course, it is important that you read definitions and theorems carefully A definition is a statement taken to be true and from which conclusions can be drawn A theorem is a conditional statement that must be proven using logical reasoning from definitions and/or other proven theorems Both definitions and theorems will state the conditions under which they can be applied Theorems can be stated in the form “if (hypotheses or conditions), then (conclusion)” In general, theorems are not reversible; that is, it is not always correct to say “if (conclusion as hypothesis), then (hypotheses as conclusion) Theorems that are “reversible” are known as bi-conditional or equivalence theorems The next two theorems are equivalence theorems 10

11. Parallel Lines THEOREM: The slopes of two lines are equal if and only if the lines are parallel Note that this is really two theorems in one: If the slopes of two lines are equal, then the lines are parallel If two lines are parallel, then the slopes of the lines are equal What this means is that we could replace the phrase “lines with equal slope” with the phrase “parallel lines” and our meaning would not change You will now see a geometric proof of this theorem 11

12. Parallel Lines We prove that, if two lines are parallel, then their slopes are equal 12

13. Parallel Lines 13

14. Parallel Lines We must also prove that, if two lines have equal slopes, then the lines are parallel In this case, we need merely reverse our steps of the proof to arrive at this conclusion So we have proven that the slopes of two lines are equal if and only if (iff) the lines are parallel 14

15. Perpendicular Lines 15

16. Perpendicular Lines 16

17. Parallel Lines 17

18. Equations of Lines 18

19. Equations of Lines 19

20. Equations of Lines 20

21. Equations of Lines 21

22. Equations of Lines 22

23. Equations of Lines 23

24. Equations of Lines 24

25. Equations of Lines 25

26. Example 2: Finding Equations of Vertical & Horizontal Lines 26

27. Example 2: Finding Equations of Vertical & Horizontal Lines 27

28. Example 3: Using the Point-Slope Equation 28

29. Example 3: Using the Point-Slope Equation 29

30. Example 4: Writing the Slope-Intercept Equation 30

31. Example 4: Writing the Slope-Intercept Equation 31

32. Example 5: Analyzing & Graphing a General Linear Equation 32

33. Example 5: Analyzing & Graphing a General Linear Equation 33

34. Example 6: Writing Equations for Lines 34

35. Example 6: Writing Equations for Lines 35

36. Example 6: Writing Equations for Lines 36

37. Example 7: Determining a Function 37 x

38. Example 7: Determining a Function 38

39. Example 8: Temperature Conversion 39

40. Example 8: Temperature Conversion 40

41. Example 8: Temperature Conversion 41

42. Chapter 1.1 Exercises Finney page 9, #1-37 odds, #40, 41, 45, 46, 57 42