Graphs and Applications of Linear Equations
Ordered Pairs
To graph ordered pairs of real numbers, we need a coordinate system.
The rectangular or Cartesian coordinate system Ordered Pairs The rectangular or Cartesian coordinate system
Ordered Pairs The rectangular or Cartesian coordinate system consists of a horizontal number line, the x-axis
Ordered Pairs The rectangular or Cartesian coordinate system consists of a horizontal number line, the x-axis and a vertical number line, the y-axis
x - axis
x x - axis
x x - axis
y - axis x x - axis
y y - axis x x - axis
y x
y x
y x
y Origin x
y Origin x
y Origin x
y P (a,b) Origin x
y P (a,b) Quadrant I Origin x
y P (a,b) Quadrant II Quadrant I Origin x
y P (a,b) Quadrant II Quadrant I Origin x Quadrant III
y P (a,b) Quadrant II Quadrant I Origin x Quadrant III Quadrant IV
Quadrant I
Quadrant I
Quadrant I
y Quadrant II Quadrant I x Quadrant III Quadrant IV
Quadrant II
Quadrant II
Quadrant II
y Quadrant II Quadrant I x Quadrant III Quadrant IV
Quadrant III
Quadrant III
Quadrant III
y Quadrant II Quadrant I x Quadrant III Quadrant IV
Quadrant IV
Quadrant IV
y Quadrant II Quadrant I x Quadrant III Quadrant IV
y Locate on the xy-plane the point corresponding to the ordered pair x
y Locate on the xy-plane the point corresponding to the ordered pair x
y Locate on the xy-plane the point corresponding to the ordered pair x
y Locate on the xy-plane the point corresponding to the ordered pair x
y Locate on the xy-plane the point corresponding to the ordered pair x
y Locate on the xy-plane the point corresponding to the ordered pair x
y Locate on the xy-plane the point corresponding to the ordered pair x
y Locate on the xy-plane the point corresponding to the ordered pair x
y Locate on the xy-plane the point corresponding to the ordered pair and tell which quadrant the point is located in x
x Quadrant I Locate on the y Locate on the xy-plane the point corresponding to the ordered pair and tell which quadrant the point is located in Quadrant I x
y Locate on the xy-plane the point corresponding to the ordered pair x
y Locate on the xy-plane the point corresponding to the ordered pair x
y Locate on the xy-plane the point corresponding to the ordered pair x
y Locate on the xy-plane the point corresponding to the ordered pair x
y Locate on the xy-plane the point corresponding to the ordered pair x
y Locate on the xy-plane the point corresponding to the ordered pair x
y Locate on the xy-plane the point corresponding to the ordered pair x
y Locate on the xy-plane the point corresponding to the ordered pair x
y Locate on the xy-plane the point corresponding to the ordered pair and tell which quadrant the point is located in x
x Quadrant III Locate on the y Locate on the xy-plane the point corresponding to the ordered pair and tell which quadrant the point is located in x Quadrant III
y Locate on the xy-plane the point corresponding to the ordered pair x
y Locate on the xy-plane the point corresponding to the ordered pair x
y Locate on the xy-plane the point corresponding to the ordered pair x
y Locate on the xy-plane the point corresponding to the ordered pair x
y Locate on the xy-plane the point corresponding to the ordered pair x
y Locate on the xy-plane the point corresponding to the ordered pair x
y Locate on the xy-plane the point corresponding to the ordered pair x
y Locate on the xy-plane the point corresponding to the ordered pair and tell which quadrant the point is located in x
x Quadrant II Locate on the y Locate on the xy-plane the point corresponding to the ordered pair and tell which quadrant the point is located in Quadrant II x
y Locate on the xy-plane the point corresponding to the ordered pair x
y Locate on the xy-plane the point corresponding to the ordered pair x
y Locate on the xy-plane the point corresponding to the ordered pair x
y Locate on the xy-plane the point corresponding to the ordered pair x
y Locate on the xy-plane the point corresponding to the ordered pair x
y Locate on the xy-plane the point corresponding to the ordered pair x
y Locate on the xy-plane the point corresponding to the ordered pair x
y Locate on the xy-plane the point corresponding to the ordered pair and tell which quadrant the point is located in x
y Locate on the xy-plane the point corresponding to the ordered pair and tell which quadrant the point is located in x
y Locate on the xy-plane the point corresponding to the ordered pair x
y Locate on the xy-plane the point corresponding to the ordered pair x
y Locate on the xy-plane the point corresponding to the ordered pair x
y Locate on the xy-plane the point corresponding to the ordered pair x
y Locate on the xy-plane the point corresponding to the ordered pair x
y Locate on the xy-plane the point corresponding to the ordered pair x
y Locate on the xy-plane the point corresponding to the ordered pair x
y Locate on the xy-plane the point corresponding to the ordered pair x
y Locate on the xy-plane the point corresponding to the ordered pair x
y Locate on the xy-plane the point corresponding to the ordered pair and tell which quadrant the point is located in x
x Quadrant IV Locate on the y Locate on the xy-plane the point corresponding to the ordered pair and tell which quadrant the point is located in x Quadrant IV
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
y Find the coordinates of the point x
Determine whether each of the following pairs is a solution of
Determine whether each of the following pairs is a solution of
Determine whether each of the following pairs is a solution of
Determine whether each of the following pairs is a solution of
Determine whether each of the following pairs is a solution of
Determine whether each of the following pairs is a solution of
Determine whether each of the following pairs is a solution of
Determine whether each of the following pairs is a solution of
Determine whether each of the following pairs is a solution of
Determine whether each of the following pairs is a solution of
Determine whether each of the following pairs is a solution of
Determine whether each of the following pairs is a solution of
Determine whether each of the following pairs is a solution of
Determine whether each of the following pairs is a solution of
Determine whether each of the following pairs is a solution of
Determine whether each of the following pairs is a solution of
Determine whether each of the following pairs is a solution of
Determine whether each of the following pairs is a solution of
Determine whether each of the following pairs is a solution of
Determine whether each of the following pairs is a solution of
Determine whether each of the following pairs is a solution of
Determine whether each of the following pairs is a solution of
Determine whether each of the following pairs is a solution of
Determine whether each of the following pairs is a solution of
Determine whether each of the following pairs is a solution of
Determine whether each of the following pairs is a solution of
Determine whether each of the following pairs is a solution of
Determine whether each of the following pairs is a solution of
Determine whether each of the following pairs is a solution of
Determine whether each of the following pairs is a solution of
Show that the pair (3,7) is a solution of the equation
Show that the pair (3,7) is a solution of the equation
Show that the pair (3,7) is a solution of the equation
Show that the pair (3,7) is a solution of the equation
Show that the pair (3,7) is a solution of the equation
Show that the pair (3,7) is a solution of the equation
Show that the pair (3,7) is a solution of the equation
Show that the pair (3,7) is a solution of the equation
Show that the pair (3,7) is a solution of the equation
Show that the pair (3,7) is a solution of the equation
Show that the pair (3,7) is a solution of the equation
Show that the pair (3,7) is a solution of the equation
Show that the pair (0,1) is a solution of the equation
Show that the pair (0,1) is a solution of the equation
Show that the pair (0,1) is a solution of the equation
Show that the pair (0,1) is a solution of the equation
Show that the pair (0,1) is a solution of the equation
Show that the pair (0,1) is a solution of the equation
Show that the pair (0,1) is a solution of the equation
Show that the pair (0,1) is a solution of the equation
Show that the pair (0,1) is a solution of the equation
Show that the pair (0,1) is a solution of the equation
Show that the pair (0,1) is a solution of the equation
Show that the pair (0,1) is a solution of the equation
Show that the pair (-3,-5) is a solution of the equation
Show that the pair (-3,-5) is a solution of the equation
Show that the pair (-3,-5) is a solution of the equation
Show that the pair (-3,-5) is a solution of the equation
Show that the pair (-3,-5) is a solution of the equation
Show that the pair (-3,-5) is a solution of the equation
Show that the pair (-3,-5) is a solution of the equation
Show that the pair (-3,-5) is a solution of the equation
Show that the pair (-3,-5) is a solution of the equation
Show that the pair (-3,-5) is a solution of the equation
Show that the pair (-3,-5) is a solution of the equation
Show that the pair (-3,-5) is a solution of the equation
Then graph the three points and use the graph to determine another pair that is a solution. y x
Then graph the three points and use the graph to determine another pair that is a solution. y x
Then graph the three points and use the graph to determine another pair that is a solution. y x
Then graph the three points and use the graph to determine another pair that is a solution. y x
Then graph the three points and use the graph to determine another pair that is a solution. y x
Then graph the three points and use the graph to determine another pair that is a solution. y x
Then graph the three points and use the graph to determine another pair that is a solution. y x
Then graph the three points and use the graph to determine another pair that is a solution. y x
Then graph the three points and use the graph to determine another pair that is a solution. y x
Then graph the three points and use the graph to determine another pair that is a solution. y x
Then graph the three points and use the graph to determine another pair that is a solution. y x
Then graph the three points and use the graph to determine another pair that is a solution. y x
Then graph the three points and use the graph to determine another pair that is a solution. y x
Then graph the three points and use the graph to determine another pair that is a solution. y x
Then graph the three points and use the graph to determine another pair that is a solution. y x
Then graph the three points and use the graph to determine another pair that is a solution. y x
Then graph the three points and use the graph to determine another pair that is a solution. y x
Then graph the three points and use the graph to determine another pair that is a solution. y x
Then graph the three points and use the graph to determine another pair that is a solution. y x
Then graph the three points and use the graph to determine another pair that is a solution. y x
Then graph the three points and use the graph to determine another pair that is a solution. y x
Then graph the three points and use the graph to determine another pair that is a solution. y x
Then graph the three points and use the graph to determine another pair that is a solution. y x
Then graph the three points and use the graph to determine another pair that is a solution. y x
Then graph the three points and use the graph to determine another pair that is a solution. y x
Then graph the three points and use the graph to determine another pair that is a solution. y x
Then graph the three points and use the graph to determine another pair that is a solution. y x
Then graph the three points and use the graph to determine another pair that is a solution. y x
Then graph the three points and use the graph to determine another pair that is a solution. y x
Then graph the three points and use the graph to determine another pair that is a solution. y x
Then graph the three points and use the graph to determine another pair that is a solution. y x
Then graph the three points and use the graph to determine another pair that is a solution. y x
Then graph the three points and use the graph to determine another pair that is a solution. y x