8/3/2019 Kii03 Ppt 03 01 Repaired]

1/12

Slide 1- 1Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

8/3/2019 Kii03 Ppt 03 01 Repaired]

2/12

Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

INTRODUCTION TO GRAPHING

Plot points associated with orderedpairs of numbers, determine the

quadrant in which a point lies.Find the coordinates of a point on agraph.

Determine whether an ordered pair is asolution of an equation with twovariables.

3.1

a

b

c

8/3/2019 Kii03 Ppt 03 01 Repaired]

3/12

Slide 1- 3Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Objective

Plot points associated with ordered

pairs of numbers, determine the

quadrant in which a point lies.

a

8/3/2019 Kii03 Ppt 03 01 Repaired]

4/12

Slide 1- 4Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Points and Ordered Pairs

To graph, or plot, points we use two perpendicular

number lines called axes. The point at which the axes

cross is called the origin. Arrows on the axes indicate

the positive directions.

Consider the pair (2, 3). The numbers in such a pair

are called the coordinates. The first coordinate in this

case is 2 and the second coordinate is 3.

8/3/2019 Kii03 Ppt 03 01 Repaired]

5/12

Slide 1- 5Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Points and Ordered Pairs continued

To plot the point (2, 3) we start

at the origin.

Move 2 units in the horizontal

direction.

The second number 3, is

positive. We move 3 units in

the vertical direction (up).

Make a dot and label the

point.

(2, 3)

(2, 3)

8/3/2019 Kii03 Ppt 03 01 Repaired]

6/12

Slide 1- 6Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Example A Plot the point (4, 3).

Solution

Starting at the origin,

we move 4 units in the

negative horizontaldirection.

The second number, 3, is

positive, so we move 3

units in the positivevertical direction (up).

3 units up

4 units left

(4, 3)

8/3/2019 Kii03 Ppt 03 01 Repaired]

7/12Slide 1- 7Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

The horizontal and vertical axes divide the plane

into four regions, or quadrants.

In which quadrant is the

point (3, 4) located?

IV

In which quadrant is thepoint (3, 4) located?

III

8/3/2019 Kii03 Ppt 03 01 Repaired]

8/12Slide 1- 8Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Objective

Find the coordinates of a point on a

graph.

b

8/3/2019 Kii03 Ppt 03 01 Repaired]

9/12Slide 1- 9Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Example BFind the coordinates of pointsA, B, C, D, E, F, and G.

SolutionPointA is 5 units to the right

of the origin and 3 units above

the origin. Its coordinates are

(5, 3). The other coordinatesare as follows:

B: (2, 4)

C: (3, 4)

D: (3,

2)E: (2, 3)

F: (3, 0)

G: (0, 2)

AB

C

D

E

F

G

8/3/2019 Kii03 Ppt 03 01 Repaired]

10/12Slide 1- 10Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Objective

Determine whether an ordered pair is

a solution of an equation with two

variables.

c

8/3/2019 Kii03 Ppt 03 01 Repaired]

11/12Slide 1- 11Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

ExampleC

Determine whether each of the following pairs is a

solution of 4y + 3x = 18: a) (2, 3); b)(1, 5).

Solutiona) We substitute 2 forx and 3 fory.

4y + 3x = 18

43+ 32 | 18

12 + 6 | 18

18 = 18 True

b) We substitute 1 forx and 5 fory.

4y + 3x = 18

45+ 31 | 18

20 + 3 | 18

23 = 18 False

Since 18 = 18is true, the pair (2, 3) is a

solution.

Since 23 = 18is false, the pair (1, 5) is

nota solution.

8/3/2019 Kii03 Ppt 03 01 Repaired]

12/12Slide 1- 12Copyright 2007 Pearson Education Inc Publishing as Pearson Addison-Wesley

Graph of An Equation

The graph of an equation is a drawing thatrepresents all its solutions.