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Rectangular Coordinate System Graphing Lines The Equation of a Line Conclusion MATH 105: Finite Mathematics 1-1: Rectangular Coordinates, Lines Prof. Jonathan Duncan Walla Walla College Winter Quarter, 2006 Rectangular Coordinate System

  1. Rectangular Coordinate System Graphing Lines The Equation of a Line Conclusion MATH 105: Finite Mathematics 1-1: Rectangular Coordinates, Lines Prof. Jonathan Duncan Walla Walla College Winter Quarter, 2006

  2. Rectangular Coordinate System Graphing Lines The Equation of a Line Conclusion Outline Rectangular Coordinate System 1 Graphing Lines 2 The Equation of a Line 3 Conclusion 4

  3. Rectangular Coordinate System Graphing Lines The Equation of a Line Conclusion Outline Rectangular Coordinate System 1 Graphing Lines 2 The Equation of a Line 3 Conclusion 4

  4. Rectangular Coordinate System Graphing Lines The Equation of a Line Conclusion Rectangular Coordinate System The Cartesian Coordinate System, also called the rectangular coordinate system, is shown below. y−axis 2nd Quadrant 1st Quadrant Origin x−axis 3rd Quadrant 4th Quadrant

  5. Rectangular Coordinate System Graphing Lines The Equation of a Line Conclusion Plotting Points Points on the coordinate system are located using an x -coordinate and y -coordinate. They are grouped together into a pair of numbers, ( x , y ). Plotting Points Plot each of the following points. P = ( − 3 , 5) P R = (2 , 0) R S S = ( − 1 , − 2)

  6. Rectangular Coordinate System Graphing Lines The Equation of a Line Conclusion Outline Rectangular Coordinate System 1 Graphing Lines 2 The Equation of a Line 3 Conclusion 4

  7. Rectangular Coordinate System Graphing Lines The Equation of a Line Conclusion Graphing a Set of Points We are particularly interested in graphing lines. A line is just a particular set of points. The Graph of a Line The graph of a line is the graph obtained by plotting all points in the set { ( x , y ) | Ax + By = C } where A , B , and C are real numbers. The General Equation of a Line The equation Ax + By = C is called the general equation of a line. A Point on a Line A point ( x 1 , y 1 ) is on the line Ax + By = C if Ax 1 + By 1 = C is a true statement.

  8. Rectangular Coordinate System Graphing Lines The Equation of a Line Conclusion Graphing a Set of Points We are particularly interested in graphing lines. A line is just a particular set of points. The Graph of a Line The graph of a line is the graph obtained by plotting all points in the set { ( x , y ) | Ax + By = C } where A , B , and C are real numbers. The General Equation of a Line The equation Ax + By = C is called the general equation of a line. A Point on a Line A point ( x 1 , y 1 ) is on the line Ax + By = C if Ax 1 + By 1 = C is a true statement.

  9. Rectangular Coordinate System Graphing Lines The Equation of a Line Conclusion Graphing a Set of Points We are particularly interested in graphing lines. A line is just a particular set of points. The Graph of a Line The graph of a line is the graph obtained by plotting all points in the set { ( x , y ) | Ax + By = C } where A , B , and C are real numbers. The General Equation of a Line The equation Ax + By = C is called the general equation of a line. A Point on a Line A point ( x 1 , y 1 ) is on the line Ax + By = C if Ax 1 + By 1 = C is a true statement.

  10. Rectangular Coordinate System Graphing Lines The Equation of a Line Conclusion Graphing a Set of Points We are particularly interested in graphing lines. A line is just a particular set of points. The Graph of a Line The graph of a line is the graph obtained by plotting all points in the set { ( x , y ) | Ax + By = C } where A , B , and C are real numbers. The General Equation of a Line The equation Ax + By = C is called the general equation of a line. A Point on a Line A point ( x 1 , y 1 ) is on the line Ax + By = C if Ax 1 + By 1 = C is a true statement.

  11. Rectangular Coordinate System Graphing Lines The Equation of a Line Conclusion Graphing a Line Since a line is nothing more than a set of points, we can graph it by determining a few of those points and then connecting them. Graphing a Line Graph the line represented by 2 x − y = 4

  12. Rectangular Coordinate System Graphing Lines The Equation of a Line Conclusion Graphing a Line Since a line is nothing more than a set of points, we can graph it by determining a few of those points and then connecting them. Graphing a Line Graph the line represented by 2 x − y = 4

  13. Rectangular Coordinate System Graphing Lines The Equation of a Line Conclusion Graphing a Line Since a line is nothing more than a set of points, we can graph it by determining a few of those points and then connecting them. Graphing a Line Graph the line represented by 2 x − y = 4 y x y 0 -4 2 0 4 4 x

  14. Rectangular Coordinate System Graphing Lines The Equation of a Line Conclusion Intercepts of a Line Graphing a line can be made a lot easier by using the following two points x -intercept The x -intercept of a line is the point at which the line crosses the x -axis, where y = 0. y -intercept The y -intercept of a line is the point at which the line crosses the y -axis, where x = 0.

  15. Rectangular Coordinate System Graphing Lines The Equation of a Line Conclusion Intercepts of a Line Graphing a line can be made a lot easier by using the following two points x -intercept The x -intercept of a line is the point at which the line crosses the x -axis, where y = 0. y -intercept The y -intercept of a line is the point at which the line crosses the y -axis, where x = 0.

  16. Rectangular Coordinate System Graphing Lines The Equation of a Line Conclusion Intercepts of a Line Graphing a line can be made a lot easier by using the following two points x -intercept The x -intercept of a line is the point at which the line crosses the x -axis, where y = 0. y -intercept The y -intercept of a line is the point at which the line crosses the y -axis, where x = 0.

  17. Rectangular Coordinate System Graphing Lines The Equation of a Line Conclusion Intercepts of a Line Graphing a line can be made a lot easier by using the following two points x -intercept The x -intercept of a line is the point at which the line crosses the x -axis, where y = 0. y -intercept The y -intercept of a line is the point at which the line crosses the y -axis, where x = 0. Finding the x and y intercepts is relatively easy and usually produces the two points needed to graph a line.

  18. Rectangular Coordinate System Graphing Lines The Equation of a Line Conclusion Graphing Lines using Intercepts Graphing Use x - and y -intercepts to graph the line 3 x + 5 y = 15. y -intercept: 3 x -intercept: 5 y x

  19. Rectangular Coordinate System Graphing Lines The Equation of a Line Conclusion Graphing Lines using Intercepts Graphing Use x - and y -intercepts to graph the line 3 x + 5 y = 15. y -intercept: 3 x -intercept: 5 y x

  20. Rectangular Coordinate System Graphing Lines The Equation of a Line Conclusion Graphing Lines using Intercepts Graphing Use x - and y -intercepts to graph the line 3 x + 5 y = 15. y -intercept: 3 x -intercept: 5 y x

  21. Rectangular Coordinate System Graphing Lines The Equation of a Line Conclusion Graphing Lines using Intercepts Graphing Use x - and y -intercepts to graph the line 7 x − 4 y = 28. y -intercept: -7 x -intercept: 4 y x

  22. Rectangular Coordinate System Graphing Lines The Equation of a Line Conclusion Graphing Lines using Intercepts Graphing Use x - and y -intercepts to graph the line 7 x − 4 y = 28. y -intercept: -7 x -intercept: 4 y x

  23. Rectangular Coordinate System Graphing Lines The Equation of a Line Conclusion Graphing Lines using Intercepts Graphing Use x - and y -intercepts to graph the line 7 x − 4 y = 28. y -intercept: -7 x -intercept: 4 y x

  24. Rectangular Coordinate System Graphing Lines The Equation of a Line Conclusion Outline Rectangular Coordinate System 1 Graphing Lines 2 The Equation of a Line 3 Conclusion 4

  25. Rectangular Coordinate System Graphing Lines The Equation of a Line Conclusion The Slope Equation The angle of a line is referred to as the slope of the line. It can be found by dividing the change in y by the change in x . Slope The slope of a line containing points ( x 1 , y 1 ) and ( x 2 , y 2 ) is m = y 2 − y 1 x 2 − x 1

  26. Rectangular Coordinate System Graphing Lines The Equation of a Line Conclusion The Slope Equation The angle of a line is referred to as the slope of the line. It can be found by dividing the change in y by the change in x . y (x ,y ) 2 2 Rise = y − y 2 1 (x ,y ) 1 1 Run = x − x 2 1 x Slope The slope of a line containing points ( x 1 , y 1 ) and ( x 2 , y 2 ) is m = y 2 − y 1 x 2 − x 1

  27. Rectangular Coordinate System Graphing Lines The Equation of a Line Conclusion The Slope Equation The angle of a line is referred to as the slope of the line. It can be found by dividing the change in y by the change in x . y (x ,y ) 2 2 Rise = y − y 2 1 (x ,y ) 1 1 Run = x − x 2 1 x Slope The slope of a line containing points ( x 1 , y 1 ) and ( x 2 , y 2 ) is m = y 2 − y 1 x 2 − x 1

  28. Rectangular Coordinate System Graphing Lines The Equation of a Line Conclusion Finding Slopes Finding Slope Find the slope of the following line. y x m = 3 − 0 0 − 5 = − 3 5

  29. Rectangular Coordinate System Graphing Lines The Equation of a Line Conclusion Finding Slopes Finding Slope Find the slope of the following line. y x m = 3 − 0 0 − 5 = − 3 5

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