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Plot ordered pairs

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... of the equation is the set of all points whose coordinates ... Plot these ordered pairs as points in the rectangular coordinate system. Point-Plotting Method ... – PowerPoint PPT presentation

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Title: Plot ordered pairs


1
Section 4.1
  • Plot ordered pairs
  • Find coordinates of points
  • Determine if an ordered pair is a solution to an
    equation
  • Find Solutions to an equation
  • Use point plotting to graph equations
  • Use linear graphs to solve problems

2
Rectangular Coordinate System
3
Locate the following points
(-3,5) (2,-4) (5,0) (0,4)
4
Ordered Pair (X,Y)
  • (m,n) means travel along the X-axis m units and
    the Y-axis n units.
  • Order matters in an ordered pair.
  • Order is alphabetical. (X,Y)

5
Solutions to Equations in Two Variables
  • When the x-coordinate is substituted for x and
    the y-coordinate is substituted for y in the
    equation, we obtain a true statement.

6
Are the following ordered pairs solutions to the
equation 3x 4y 12 ?
  • (4,0)
  • (8,-3)
  • (1,2)

7
Are the following ordered pairs solutions to the
equation 3x 4y 12 ?
  • (4,0) Substitute 4 for x and 0 for y

8
Are the following ordered pairs solutions to the
equation 3x 4y 12 ?
  • (4,0) Substitute 4 for x and 0 for y
  • 3x 4y 12 original equation

9
Are the following ordered pairs solutions to the
equation 3x 4y 12 ?
  • (4,0) Substitute 4 for x and 0 for y
  • 3x 4y 12 original equation
  • 3(4) 4(0) substitution

10
Are the following ordered pairs solutions to the
equation 3x 4y 12 ?
  • (4,0) Substitute 4 for x and 0 for y
  • 3x 4y 12 original equation
  • 3(4) 4(0) substitution
  • 12 0 simplify

11
Are the following ordered pairs solutions to the
equation 3x 4y 12 ?
  • (4,0) Substitute 4 for x and 0 for y
  • 3x 4y 12 original equation
  • 3(4) 4(0) substitution
  • 12 0 simplify
  • 12 verify

12
Are the following ordered pairs solutions to the
equation 3x 4y 12 ?
  • (4,0) Substitute 4 for x and 0 for y
  • 3x 4y 12 original equation
  • 3(4) 4(0) substitution
  • 12 0 simplify
  • 12 verify
  • (4,0) is a solution to the equation

13
Are the following ordered pairs solutions to the
equation 3x 4y 12 ?
  • (8,-3) Substitute 8 for x and -3 for y

14
Are the following ordered pairs solutions to the
equation 3x 4y 12 ?
  • (8,-3) Substitute 8 for x and -3 for y
  • 3x 4y 12 original equation

15
Are the following ordered pairs solutions to the
equation 3x 4y 12 ?
  • (8,-3) Substitute 8 for x and -3 for y
  • 3x 4y 12 original equation
  • 3(8) 4(-3) substitution

16
Are the following ordered pairs solutions to the
equation 3x 4y 12 ?
  • (8,-3) Substitute 8 for x and -3 for y
  • 3x 4y 12 original equation
  • 3(8) 4(-3) substitution
  • 24 -12 simplify
  • 12 verify

17
Are the following ordered pairs solutions to the
equation 3x 4y 12 ?
  • (8,-3) Substitute 8 for x and -3 for y
  • 3x 4y 12 original equation
  • 3(8) 4(-3) substitution
  • 24 -12 simplify
  • 12 verify
  • (8,-3) is a solution to the equation

18
Are the following ordered pairs solutions to the
equation 3x 4y 12 ?
  • (1,2) Substitute 1 for x and 2 for y

19
Are the following ordered pairs solutions to the
equation 3x 4y 12 ?
  • (1,2) Substitute 1 for x and 2 for y
  • 3x 4y 12 original equation

20
Are the following ordered pairs solutions to the
equation 3x 4y 12 ?
  • (1,2) Substitute 1 for x and 2 for y
  • 3x 4y 12 original equation
  • 3(1) 4(2) substitution

21
Are the following ordered pairs solutions to the
equation 3x 4y 12 ?
  • (1,2) Substitute 1 for x and 2 for y
  • 3x 4y 12 original equation
  • 3(1) 4(2) substitution
  • 3 8 simplify

22
Are the following ordered pairs solutions to the
equation 3x 4y 12 ?
  • (1,2) Substitute 1 for x and 2 for y
  • 3x 4y 12 original equation
  • 3(1) 4(2) substitution
  • 3 8 simplify
  • 11 verify

23
Are the following ordered pairs solutions to the
equation 3x 4y 12 ?
  • (1,2) Substitute 1 for x and 2 for y
  • 3x 4y 12 original equation
  • 3(1) 4(2) substitution
  • 3 8 simplify
  • 11 verify
  • (1,2) is NOT a solution to the equation

24
  • We can now determine if a given ordered pair is a
    solution to an equation.
  • But how do we create our own ordered pairs that
    are solutions to an equation?

25
Finding Solutions to an Equation
  • Select a value for one of the variables

26
Finding Solutions to an Equation
  • Select a value for one of the variables
  • Substitute that value into the equation and find
    the corresponding value of the other variable.

27
Finding Solutions to an Equation
  • Select a value for one of the variables
  • Substitute that value into the equation and find
    the corresponding value of the other variable.
  • Use the values of the two variables to form an
    ordered pair (x,y). This pair is a solution to
    the equation.

28
Find 5 solutions to y 3x - 2
29
Find 5 solutions to y 3x - 2
30
Find 5 solutions to y 3x - 2
31
Find 5 solutions to y 3x - 2
32
Find 5 solutions to y 3x - 2
33
Find 5 solutions to y 3x - 2
34
Find 5 solutions to y 3x - 2
35
  • We can now determine if a given ordered pair is a
    solution to an equation. We can now find our own
    solutions to an equation.
  • How do we graph linear equations?

36
Graphing Linear Equations
  • We found 5 solutions to the equation y
    3x 2.

37
Graphing Linear Equations
  • We found 5 solutions to the equation y
    3x 2.
  • We can find an infinite number of solutions to y
    3x 2.

38
Graphing Linear Equations
  • We found 5 solutions to the equation y
    3x 2.
  • We can find an infinite number of solutions to y
    3x 2.
  • The graph of the equation is the set of all
    points whose coordinates satisfy the equation.

39
Point-Plotting Method
  • Find several ordered pairs that are solutions to
    your equation.

40
Point-Plotting Method
  • Find several ordered pairs that are solutions to
    your equation.
  • Plot these ordered pairs as points in the
    rectangular coordinate system.

41
Point-Plotting Method
  • Find several ordered pairs that are solutions to
    your equation.
  • Plot these ordered pairs as points in the
    rectangular coordinate system.
  • Connect the points with a smooth curve or line.

42
Point-Plotting Method
  • Step 1 Find ordered pairs that are solutions to
    the equation y 2x 1

43
Point-Plotting Method
  • Step 1 Find ordered pairs that are solutions to
    the equation y 2x 1

44
Point-Plotting Method
  • Step 1 Find ordered pairs that are solutions to
    the equation y 2x 1

45
Point-Plotting Method
  • Step 1 Find ordered pairs that are solutions to
    the equation y 2x 1

46
Point-Plotting Method
  • Step 1 Find ordered pairs that are solutions to
    the equation y 2x 1

47
Point-Plotting Method
  • Step 1 Find ordered pairs that are solutions to
    the equation y 2x 1

48
Point-Plotting Method
  • Step 1 Find ordered pairs that are solutions to
    the equation y 2x 1

49
Point-Plotting Method
  • Step 1 Find ordered pairs that are solutions to
    the equation y 2x 1.
  • We found (-2,-3),(-1,-1),(0,1),(1,3),(2,5).
  • Now plot these points on a rectangular coordinate
    system and connect them with a line.

50
Lines of the form y mx b
51
Comparing graphs of the form y mx b
  • If the value of m does not change
  • The graph of y mx b is the graph y
    mx shifted b units up or down (
    shifts the graph up, - shifts the graph down).
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