1. College Algebra Chapter 2 Functions and Graphs
Section 2.1
The Rectangular Coordinate System and Graphing Utilities

2. 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. Example 1:
Plot each point.
a b.
c d.
e f.

4. 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

5. Distance Formula
The distance between points (x1, y1) and (x2, y2)
is given by:

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

7. 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.

8. Example 4:
Find the exact distance between the points
and

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

10. Example 5 continued:
A ( –2 , 1 ) B ( 2 , 5 ) C ( 5 , 2 )

11. Midpoint Formula
The midpoint of the line segment with endpoints (x1, y1) and (x2, y2) is:

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

13. 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

14. Graph the equation by plotting points x y
Example 7:
Graph the equation by plotting points x y
Ordered Pairs

15. Graph the equation by plotting points x y
Example 8:
Graph the equation by plotting points x y
Ordered Pairs

16. Graph the equation by plotting points x y
Example 9:
Graph the equation by plotting points x y
Ordered Pairs

17. Graph the equation by plotting points x y
Example 10:
Graph the equation by plotting points x y
Ordered Pairs

18. 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

19. Example 11:
Estimate the x- and y-intercepts from the graph.
x-int: ____________ y-int: ____________

20. Example 12:
Estimate the x- and y-intercepts from the graph.
x-int: ____________ y-int: ____________

21. Example 13:
Find the x- and y-intercepts.

22. Example 14:
Find the x- and y-intercepts.

23. Example 15:
Find the x- and y-intercepts.

24. 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

25. Graph Equations Using a Graphing Utility
Enter the equation into the graphing editor in the form Y = ____________

26. Graph Equations Using a Graphing Utility, continued
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]

27. Graph Equations Using a Graphing Utility, continued
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.

28. Example 16:
Graph on the standard viewing window.
Make a table beginning at x = 0 with Tbl = 2. X Y1

29. Example 17:
Graph on the standard viewing window.
Make a table beginning at x = –2 with Tbl = 1. X Y1

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

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