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).