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Section 1.1 Rectangular Coordinates;  Graphing Utilities; Introduction to Graphing Equations
SECTION 1.1 OBJECTIVES 1. Use the Distance Formula 2. Use the Midpoint Formula 3. Graph Equations by Hand by Plotting Poin...
Rectangular or Cartesian Coordinate System  Rectangular Coordinat es x axis y axis origin
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 plo...
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
Coordinat e Axis on Graphing Utility
Coordinate Axis on Graphing Utility
Coordinate Axis on Graphing Utility
Point on Axis on Graphing Utility
Find the coordinates of the point shown.  Assume the coordinates are integers. (- 2, 2)
OBJECTIVE 1
Horizontal or Vertical Segments The Distance between two points is the absolute value of their difference
Not every pair of points lies on a vertical or horizontal line so the distance formula must be used.
 
Find the distance  d   between the points (2, 5) and (4, 8)
Find the length of the line segment shown.
a.  A  = ( –  4,  –  1),  B  = (1, 11), and  C  = (1,  –  1)
<ul><li>Length of AB= 13 </li></ul><ul><li>Length of BC= 12 </li></ul><ul><li>Length of AC= 5  </li></ul>c.  d.  A  = ( – ...
OBJECTIVE 2
Development of Midpoint Formula
 
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 mid...
OBJECTIVE 3
Example of Data Plotted by Hand
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)
Steps to Graph an Equation by Hand by Plotting Points 1.  Find all points (x, y) that satisfy the equation.  To determine ...
X Y -2 1 -1 3 0 5 1 7 2 9
X Y -2 - 8 -1 <ul><li>1 </li></ul>0 0 1 1 2 8
OBJECTIVE 4
Steps for Graphing an Equation Using a Graphing Utility 1.  Solve the equation for y in terms of x 2.  Enter the equation ...
 
Solve for  y :  –  2 x  + 5 y  + 3 =  –  1
 
OBJECTIVE 5
 
OBJECTIVE 6
Intercepts of a Graph
X-intercepts are: (- 3, 0 ), (4.5, 0), (3/2, 0) Y-intercepts are (0, - 3.5), (0, - 4/3), (0, 3) .
OBJECTIVE 7
Approximating Intercepts Using a Graphing Utility 1.  Use 2 nd  Calc, Value on the TI-83/84 calculator to find the y-inter...
 
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Rectangular Coordinates, Introduction to Graphing Equations

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  • College Algebra: Graphing and Data Analysis
    Questions: Find all points having an x-coordinates of 2 whose distance from the point (-2, -1) is 5. How can I solve College Algebra?
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Transcript of "Rectangular Coordinates, Introduction to Graphing Equations"

  1. 1. Section 1.1 Rectangular Coordinates; Graphing Utilities; Introduction to Graphing Equations
  2. 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. 3. Rectangular or Cartesian Coordinate System Rectangular Coordinat es x axis y axis origin
  4. 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. 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. 6. Coordinat e Axis on Graphing Utility
  7. 7. Coordinate Axis on Graphing Utility
  8. 8. Coordinate Axis on Graphing Utility
  9. 9. Point on Axis on Graphing Utility
  10. 10. Find the coordinates of the point shown. Assume the coordinates are integers. (- 2, 2)
  11. 11. OBJECTIVE 1
  12. 12. Horizontal or Vertical Segments The Distance between two points is the absolute value of their difference
  13. 13. Not every pair of points lies on a vertical or horizontal line so the distance formula must be used.
  14. 15. Find the distance d between the points (2, 5) and (4, 8)
  15. 16. Find the length of the line segment shown.
  16. 17. a. A = ( – 4, – 1), B = (1, 11), and C = (1, – 1)
  17. 18. <ul><li>Length of AB= 13 </li></ul><ul><li>Length of BC= 12 </li></ul><ul><li>Length of AC= 5 </li></ul>c. d. A = ( – 4, – 1), B = (1, 11), and C = (1, – 1)
  18. 19. OBJECTIVE 2
  19. 20. Development of Midpoint Formula
  20. 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.
  21. 23. OBJECTIVE 3
  22. 24. Example of Data Plotted by Hand
  23. 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)
  24. 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.
  25. 27. X Y -2 1 -1 3 0 5 1 7 2 9
  26. 28. X Y -2 - 8 -1 <ul><li>1 </li></ul>0 0 1 1 2 8
  27. 29. OBJECTIVE 4
  28. 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
  29. 32. Solve for y : – 2 x + 5 y + 3 = – 1
  30. 34. OBJECTIVE 5
  31. 36. OBJECTIVE 6
  32. 37. Intercepts of a Graph
  33. 38. X-intercepts are: (- 3, 0 ), (4.5, 0), (3/2, 0) Y-intercepts are (0, - 3.5), (0, - 4/3), (0, 3) .
  34. 39. OBJECTIVE 7
  35. 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.
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