Slide 1Copyright © 2015, 2011, 2008 Pearson Education, Inc.

The Rectangular Coordinate System

and Paired Data

Section 8.3

Slide 2Copyright © 2015, 2011, 2008 Pearson Education, Inc.

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, y-coordinate.

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.

Slide 3Copyright © 2015, 2011, 2008 Pearson Education, Inc.

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).

Graphing an Ordered Pair

Slide 4Copyright © 2015, 2011, 2008 Pearson Education, Inc.

Note that the order of the coordinates is very important, since (–4, 2) and (2, –4) are located in different positions.

x-axis

y-axis

(5, 3)

5 units right

3 units up

(0, 5)

(–6, 0)

(2, –4)

(–4, 2)

(0, 0)

Quadrant I

Quadrant IVQuadrant III

Quadrant II

origin

Graphing an Ordered Pair

Slide 5Copyright © 2015, 2011, 2008 Pearson Education, Inc.

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.

Helpful Hint

Slide 6Copyright © 2015, 2011, 2008 Pearson Education, Inc.

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)

Example

Slide 7Copyright © 2015, 2011, 2008 Pearson Education, Inc.

Example

Find the ordered pair corresponding to each point plotted below.

A

B

C

D

E

F

Slide 8Copyright © 2015, 2011, 2008 Pearson Education, Inc.

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.

Completing Ordered Pair Solutions

Slide 9Copyright © 2015, 2011, 2008 Pearson Education, Inc.

Example

Is (0, –4) a solution of the equation x + 3y = –12?

Slide 10Copyright © 2015, 2011, 2008 Pearson Education, Inc.

Complete each ordered pair solution of the equation y = −5x.a. (5, ) b. ( , 0) c. (–3, )

Example

Slide 11Copyright © 2015, 2011, 2008 Pearson Education, Inc.

Complete teach ordered pair solution of the equation y = 5x + 2.a. (0, ) b. (0, –3)

Example