Title: Plot ordered pairs
1Section 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
2Rectangular Coordinate System
3Locate the following points
(-3,5) (2,-4) (5,0) (0,4)
4Ordered 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)
5Solutions 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.
6Are the following ordered pairs solutions to the
equation 3x 4y 12 ?
7Are the following ordered pairs solutions to the
equation 3x 4y 12 ?
- (4,0) Substitute 4 for x and 0 for y
-
8Are 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
-
9Are 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
10Are 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
11Are 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
12Are 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
13Are the following ordered pairs solutions to the
equation 3x 4y 12 ?
- (8,-3) Substitute 8 for x and -3 for y
-
-
14Are 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
-
15Are 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
-
16Are 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
-
17Are 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
18Are the following ordered pairs solutions to the
equation 3x 4y 12 ?
- (1,2) Substitute 1 for x and 2 for y
-
-
19Are 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
-
-
20Are 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
-
-
21Are 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
-
-
-
22Are 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
-
-
23Are 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?
25Finding Solutions to an Equation
- Select a value for one of the variables
26Finding 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.
27Finding 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.
28Find 5 solutions to y 3x - 2
29Find 5 solutions to y 3x - 2
30Find 5 solutions to y 3x - 2
31Find 5 solutions to y 3x - 2
32Find 5 solutions to y 3x - 2
33Find 5 solutions to y 3x - 2
34Find 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?
36Graphing Linear Equations
- We found 5 solutions to the equation y
3x 2.
37Graphing Linear Equations
- We found 5 solutions to the equation y
3x 2. - We can find an infinite number of solutions to y
3x 2.
38Graphing 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.
39Point-Plotting Method
- Find several ordered pairs that are solutions to
your equation.
40Point-Plotting Method
- Find several ordered pairs that are solutions to
your equation. - Plot these ordered pairs as points in the
rectangular coordinate system.
41Point-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.
42Point-Plotting Method
- Step 1 Find ordered pairs that are solutions to
the equation y 2x 1
43Point-Plotting Method
- Step 1 Find ordered pairs that are solutions to
the equation y 2x 1
44Point-Plotting Method
- Step 1 Find ordered pairs that are solutions to
the equation y 2x 1
45Point-Plotting Method
- Step 1 Find ordered pairs that are solutions to
the equation y 2x 1
46Point-Plotting Method
- Step 1 Find ordered pairs that are solutions to
the equation y 2x 1
47Point-Plotting Method
- Step 1 Find ordered pairs that are solutions to
the equation y 2x 1
48Point-Plotting Method
- Step 1 Find ordered pairs that are solutions to
the equation y 2x 1
49Point-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.
50Lines of the form y mx b
51Comparing 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).