1. Section 1.1 Rectangular Coordinates; Graphing Utilities; Introduction to Graphing Equations

2. SECTION 1.1 OBJECTIVES 1. Use the Distance Formula 2. Use the Midpoint Formula 3. Graph Equations by Hand by Plotting Points 4. Graph Equations Using a Graphing Utility 5. Use a Graphing Utility to Create Tables 6. Find Intercepts from a Graph 7. Use a Graphing Utility to Approximate Intercepts

3. Rectangular or Cartesian Coordinate System Rectangular Coordinat es x axis y axis origin

4. Let's plot the point (6,4) (-3,-5) (0,7) Let's plot the point (-6,0) (6,4) (-6,0) Let's plot the point (-3,-5) Let's plot the point (0,7) Rectangular Coordinat es

5. Quadrant I x > 0, y > 0 Quadrant II x < 0, y > 0 Quadrant III x < 0, y < 0 Quadrant IV x > 0, y < 0 Coordinat e Axis

6. Coordinat e Axis on Graphing Utility

7. Coordinate Axis on Graphing Utility

8. Coordinate Axis on Graphing Utility

9. Point on Axis on Graphing Utility

10. Find the coordinates of the point shown. Assume the coordinates are integers. (- 2, 2)

11. OBJECTIVE 1

12. Horizontal or Vertical Segments The Distance between two points is the absolute value of their difference

13. Not every pair of points lies on a vertical or horizontal line so the distance formula must be used.

15. Find the distance d between the points (2, 5) and (4, 8)

16. Find the length of the line segment shown.

17. a. A = ( – 4, – 1), B = (1, 11), and C = (1, – 1)

19. OBJECTIVE 2

20. Development of Midpoint Formula

22. Find the midpoint of a line segment from P 1 = (3, -5) to P 2 = (1, 7). Plot the points P 1 and P 2 and their midpoint.

23. OBJECTIVE 3

24. Example of Data Plotted by Hand

25. Determine if the following points are on the graph of the equation - 3 x + y = 6 (b) (2, 0) (a) (0, 4) (c) (-1, 3)

26. Steps to Graph an Equation by Hand by Plotting Points 1. Find all points (x, y) that satisfy the equation. To determine these points, choose values of x and use the equation to find the corresponding values for y. Create a table of values. 2. Plot the points listed in the table. Now connect the points to obtain the graph of the equation.

27. X Y -2 1 -1 3 0 5 1 7 2 9

29. OBJECTIVE 4

30. Steps for Graphing an Equation Using a Graphing Utility 1. Solve the equation for y in terms of x 2. Enter the equation to be graphed into your graphing utility. (y= editor) 3. Choose an initial viewing window. Without any knowledge about the behavior of the graph, it is common to choose the standard viewing window as the initial viewing window. 4. Graph the equation 5. Adjust the viewing window until a complete graph is obtained

32. Solve for y : – 2 x + 5 y + 3 = – 1

34. OBJECTIVE 5

36. OBJECTIVE 6

37. Intercepts of a Graph

38. X-intercepts are: (- 3, 0 ), (4.5, 0), (3/2, 0) Y-intercepts are (0, - 3.5), (0, - 4/3), (0, 3) .

39. OBJECTIVE 7

40. Approximating Intercepts Using a Graphing Utility 1. Use 2 nd Calc, Value on the TI-83/84 calculator to find the y-intercept by entering 0 for the x-value. 2. Use 2 nd Calc, Zero on the TI-83/84 calculator to find the x-intercept. See the owners’ manual for specific instructions. 3. For other calculators, check your owners’ manual.