1. College Algebra Chapter 2 Functions and Graphs
Section 2.1
The Rectangular Coordinate System and Graphing Utilities
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2. Concepts
1. Plot Points on a Rectangular Coordinate System 2. Use the Distance and Midpoint Formulas 3. Graph Equations by Plotting Points 4. Identify x- and y-Intercepts 5. Graph Equations Using a Graphing Utility

3. Concept 1 Plot Points on a Rectangular Coordinate System

4. Example 1
Plot each point.

5. Concept 2 Use the Distance and Midpoint Formulas

6. Distance Formula
The distance between points

7. Example 2
Find the distance between the points (–3, –4) and (3, 0). Give the exact distance and an approximation to 2 decimal places. Solution:

8. Example 3
Find the distance between the points (–1.2, 4.5) and (3.8, 1.5). Give the exact distance and an approximation to 2 decimal places. Solution:

9. Example 4
Solution:

10. Skill Practice 1
Find the distance between the points (-1,4) and (3,-6). Give exact distance and an approximation to 2 decimal places.

11. Example 5 (1 of 2)
Determine if the given points form the vertices of a right triangle: A(-2,1) B(2,5) C(5,2)

12. Example 5 (2 of 2)

13. Skill Practice 2
Determine if the points X(-6, -4), Y(2, -2), and Z(0, 5) form the vertices of a right triangle.

14. Midpoint Formula
The midpoint of the line segment with endpoints

15. Example 6
Find the midpoint of the line segment with endpoints (–1.8, –3) and (4.5, –1).

16. Skill Practice 3
Find the midpoint of the line segment with endpoints (-1.5, -9) and (-8.7, 4).

17. Concept 3 Graph Equations by Plotting Points

18. Example 7 (1 of 2) Graph the equation by plotting points X Y
Ordered Pairs 3
(0,3) 1 4
(1,4) 2 7
(2,7) 12
(3,12) -1
(-1,4) -2
(-2,7)

19. Example 7 (2 of 2)

20. Example 8 (1 of 2)
Graph the equation by plotting points

21. Example 8 (2 of 2)

22. Skill Practice 4
Graph the equation by plotting points.

23. Example 9 (1 of 2)
Graph the equation by plotting points x =|y - 4| Pick y first x Y
Ordered Pairs
|-3| 1
(3,1)
|-2| 2
(2,2)
|-1| 3
(1,3)
|0| 4
(0,4)
|1| 5
(1,5)
|2| 6
(2,6)

24. Example 9 (2 of 2)

25. Example 10 (1 of 2) Graph the equation by plotting points X Y
Ordered Pairs -2
(-2,0) -1 1
(-1,1) 2
(2,2) 7 3
(7,3)
(-1,-1)
(2,-2)

26. Example 10 (2 of 2)

27. Skill Practice 5
Graph the equation by plotting points.

28. Concept 4 Identify x- and y-Intercepts

29. Example 11
Estimate the x- and y-intercepts from the graph. x-int: ____________ y-int:____________
Solution: x-int: (3,0) y-int: (0,3)

30. Example 12
Estimate the x- and y-intercepts from the graph. x-int: ____________ y-int:____________
Solution:
x-int: (2,0) (-2,0)
y-int: (0,-4)

31. Example 13
Find the x- and y-intercepts.
Solution:

32. Example 14
Find the x- and y-intercepts. y = |y - 3| + 2 Solution: x-intercept: x =|0-3| + 2 = |-3| + 2 = = 5 (5,0) y-intercept: 0 = |y - 3| = |y - 3| No Solution. No y - intercept

33. Example 15 (1 of 2)
Find the x- and y-intercepts.
Solution:

34. Example 15 (2 of 2)

35. Skill Practice 6 Given the equation Find the x-intercept(s).
Find the y-intercept(s).

36. Concept 5 Graph Equations Using a Graphing Utility

37. Graph Equations Using a Graphing Utility (1 of 3)
Enter the equation into the graphing editor in the form Y =____________

38. Graph Equations Using a Graphing Utility (2 of 3)
The standard viewing window is from –10 to 10 on the x-axis and –10 to 10 on the y-axis. The tick marks on each axis are 1 unit apart. This viewing window would be listed: [–10, 10, 1] by [–10, 10, 1]

39. Graph Equations Using a Graphing Utility (3 of 3)
To set up a table, enter the starting value for x and the increment of change for x. In this case, || Tbl = 1 means the x-value will change in steps of 1 unit. 1, 2, 3, ... etc.

40. Example 16 (1 of 2)
Graph on the standard viewing window. Make a table beginning at x = 0 with ||Tbl = 2. y = 0.5x + 2

41. Example 16 (2 of 2) X Y1 2 3 4 6 5 8 10 7

42. Example 17 (1 of 2)
Graph on the standard viewing window. Make a table beginning at x = –2 with || Tbl = 1.

43. Example 17 (2 of 2) X Y1 -2 8 -1 9 1 5 2 3 -7

44. Example 18
Graph on the given viewing window [–3, 8, 1] by [–30, 25, 5]

45. Example 19
Graph on the given viewing window [–5, 5, 1] by [–1, 10, 1]

46. Skill Practice 7 Use a graphing utility to graph y = -x + 2 and
on the viewing window [-6, 6, 1] by [-4, 8, 1].