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Section 8.3
The Rectangular
Coordinate System
and Paired Data
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Slide 1
The Rectangular Coordinate System
Ordered pair – two numbers associated with a point on a graph.
The first number gives the horizontal location of the point. The
second gives the vertical location.
Coordinate – a number in an ordered pair; x-coordinate, ycoordinate.
x-axis – horizontal number line
y-axis –vertical number line
Origin – point of intersection of the two axes
Quadrants – four regions created by the intersection of the two
axes.
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Slide 2
Graphing an Ordered Pair
To graph the point corresponding to a particular
ordered pair (a, b), you must start at the origin
and move a units to the left or right (right if a is
positive, left if a is negative), then move b units
up or down (up if b is positive, down if b is
negative).
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Slide 3
Graphing an Ordered Pair
y-axis
Quadrant I
Quadrant II
(0, 5)
(5, 3)
(–4, 2)
3 units up
(0, 0)
(–6, 0)
x-axis
5 units right
origin
(2, –4)
Quadrant III
Note that the
order of the
coordinates is
very important,
since (–4, 2)
and (2, –4) are
located in
different
positions.
Quadrant IV
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Slide 4
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.
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Slide 5
Example
Plot each ordered pair on the same set of axes.
a. (4, 2)
b. (‒3, ‒2)
c. (2, ‒3)
d. (0, 4)
e. (5, 0)
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Slide 6
Example
Find the ordered pair corresponding to each point
plotted below.
A
F
B
C
D
E
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Slide 7
Completing Ordered Pair Solutions
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.
If you know one coordinate of an ordered pair
that is a solution for an equation, you can find
the other coordinate through substitution and
solving the resulting equation.
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Slide 8
Example
Is (0, –4) a solution of the equation x + 3y = –12?
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Slide 9
Example
Complete each ordered pair solution of the
equation y = −5x.
a. (5, )
b. ( , 0)
c. (–3, )
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Slide 10
Example
Complete teach ordered pair solution of the
equation y = 5x + 2.
a. (0, )
b. (0, –3)
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Slide 11