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Section 8.3
The Rectangular Coordinate
System and Paired Data
The Rectangular Coordinate System
y-axis
5
quadrant II 4
quadrant I
3
2
origin
1
(0,0)
-5 -4 -3 -2 -1
1 2 3 4 5
-2
-3
quadrant III - 4
quadrant IV
-5
x-axis
2
Plotting Points
y
5
4
3
2
1
(4,3)
x
-5 -4 -3 -2 -1
1 2 3 4 5
-2
-3
-4
-5
3
In general, to plot the ordered pair (x,y), start
at the origin. Next,
(x,y)
move x units left or right and then move y
units up or down.
right if x is positive,
left if x is negative
up if y is positive,
down if y is negative
Martin-Gay, Prealgebra, 5ed
4
Helpful Hint
Since the first number, or x-coordinate, of an
ordered pair is associated with the x-axis, it
tells how many units to move left or right.
Similarly, the second number, or y-coordinate,
tells how many units to move up or down.
Martin-Gay, Prealgebra, 5ed
5
Plot (2,1), (-3,4), (5,0), (0,-2), (1,-3), and (-4,-5).
y
(-3,4)
5
4
3
2
1
(2,1)
(5,0)
x
-5 -4 -3 -2 -1
-2
-3
(-4,-5)-4
-5
1 2 3 4 5
(0,-2)
(1,-3)
6
Helpful Hint
Remember that each point in the
rectangular coordinate system
corresponds to exactly one ordered pair
and that each ordered pair corresponds
to exactly one point.
Martin-Gay, Prealgebra, 5ed
7
Helpful Hint
If an ordered pair has a y-coordinate of
0, its graph lies on the x-axis. If an
ordered pair has an x-coordinate of 0,
its graph lies on the y-axis.
Order is the key word in ordered pair.
The first value always corresponds to
the x-value and the second value always
corresponds to the y-value.
Martin-Gay, Prealgebra, 5ed
8
Completing Ordered Pair Solutions
An equation in two variables, such as
3x + y = 9, has solutions consisting of
two values, one for x and one for y.
For example, x = 1 and y = 6 is a
solution of 3x + y = 9, because, if x is
replaced with 1 and y is replaced with
6, we get a true statement.
3x + y = 9
?
3(1) + 6 = 9
9=9
True
The solution x = 1
and y = 6 can be
written as (1,6), an
ordered pair of
numbers.
Martin-Gay, Prealgebra, 5ed
9
In general, an ordered pair is a solution
of an equation in two variables if
replacing the variables by the values of
the ordered pair results in a true
statement.
Martin-Gay, Prealgebra, 5ed
10
If the x-value of an ordered pair is known,
then the y-value can be determined, and
vice-versa.
Complete each ordered pair so that it is
a solution to the equation 2x - y = 6.
(0, )
( , 4)
Let x = 0 and
solve for y.
2x - y = 6
2(0) - y = 6
0-y=6
y=-6
The ordered pair is (0,- 6).
Let y = 4 and
solve for x.
2x - y = 6
2x - 4 = 6
2x = 10
x=5
The ordered pair is (5,4).
11
Helpful Hint
Have you noticed?
Equations in two variables can have more
than one solution.
Martin-Gay, Prealgebra, 5ed
12