Wir2.5• LESSON

PLOTTING POINTS = JUST LIKE BATTLESHIP

Notebook File

4-1 Coordinates and Scatter Plots

• Coordinate Plane = a grid formed by two numbers lines, one vertical, the other horizontal

• Ex:

• Axes = the 2 #lines that define a coordinate plane. The horizontal # line is the x-axis and the vertical # line is the y-axis

• Origin = the point where the x- and y-axes meet in a coordinate plane

• Quadrants = the four sections formed by the axes in a coordinate plane

• Ordered Pair = 2 #s used together to designate a particular point in a coordinate plane. The 1st # is the x-coordinate and the 2nd # is the y-coordinate. (x, y)

• example (2, -3): x = 2, y = 3 so go to the right 2 and down 3!

• Coordinates = the 2#s in an ordered pair

• Scatterplot = real-life situation comparing relationship btwn 2 quantities & graph the pairs on a coordinate axis

Use the coordinate plane at the right to write the coordinates of each point.

1.) A

2.) B

3.) C

4.) D

5.) E

6.) F

7.) G

8.) H

EXAMPLE 1 Name points in a coordinate plane

Graph each given point on the axes on your worksheet.

1.) J = (6, 2)

2.) K = (-3, -5)

3.) L = (-1, 5)

4.) M = (0, 5)

5.) N = (4, 0)

6.) P = (-5, 0)

7.) R = (-5, -3)

8.) S = (6, -1)

EXAMPLE 2 Plot points in a coordinate plane

Make a table by substituting the domain values into the function.

STEP 1SOLUTION

Graph the function y = 2x – 1 with domain –2, –1, 0, 1, and 2. Then identify the range of the function.

EXAMPLE 3 Graph a function

STEP 2

List the ordered pairs: (–2, –5), (–1, –3), (0, –1), (1, 1), (2, 3). Then graph the function.

STEP 3Identify the range. The range consists of the y-values from the table: –5, –3, –1, 1, and 3.

GUIDED PRACTICE for Examples 2 and 3

Plot the point in a coordinate plane. Describe thelocation of the point.

1. A(2, 5)

2. B(–1, 0)

3. C(– 2, –1)

x-axisANSWER

Quadrant IIIANSWER

Quadrant IANSWER

4. D(–5, 3)

Quadrant IIANSWER

GUIDED PRACTICE for Examples 2 and 3

5. Graph the function y = – x + 2 with domain –6, –3, 0, 3, and 6. Then identify the range of the function.

13

range: 0, 1, 2, 3, and 4ANSWER

Plot the point in a coordinate plane. Describe thelocation of the point.

Graph a function represented by a table

EXAMPLE 4

VOTING In 1920 the ratification of the 19th amendment to the United States Constitution gave women the right to vote. The table shows the number (to the nearest million) of votes cast in presidential elections both before and since women were able to vote.

Explain how you know that the table represents a function.

a.

Graph the function represented by the table.b.

Describe any trend in the number of votes cast.c.

Years before orsince 1920

–12 –8 –4 0 4 8 12

Votes (millions) 15 15 19 27 29 37 40

Graph a function represented by a table

EXAMPLE 4

SOLUTION

The table represents a function because each input has exactly one output.

a.

To graph the function, let x be the number of years before or since 1920. Let y be the number of votes cast (in millions).

b.

The graph of the function is shown.In the three election years before 1920, the number of votes cast was less than 20 million. In 1920, the number of votes cast was greater than 20 million. The number of votes cast continued to increase in the three election years since 1920.

c.

GUIDED PRACTICE for Example 4

6. The presidential election in 1972 was the first election in which 18-year-olds were allowed to vote. The table shows the number (to the nearest million) of votes cast in presidential elections both before and since 1972.

VOTING

Years before orsince 1972

–12 –8 –4 0 4 8 12

Votes (millions) 69 71 73 78 82 87 93

a. Explain how you know the graph represents a function.

The table represents a function because each input has exactly one output.

ANSWER

GUIDED PRACTICE for Example 4

b. Graph the function represented by the table.ANSWER

c. Describe any trend in the number of votes cast.

Sample answer: Before 1972, the number of votes cast increased by 2 million every 4 years. In 1972, the number increased by 5 million and continued to increase by more than 2 million every four years since 1972.

ANSWER

Summary• In the ordered pair (4,9), the x-coordinate is ---------.• Ans: x is 4, y is 9• Decide whether the following statement is true or false.

Each point in a coordinate plane corresponds to an ordered pair of real numbers.

• Ans: True• Write the ordered pairs that correspond to the points labeled A, B, and C in the coordinateplane at the right.

Ans: A = (1,1) B = (-2,1) c = (0, -2)

Check Yourself

Pg. 209-212 #4-12e, 13-18, 23,24, 26, 36, 42-43

Extra credit:- Graphiti drawing with points plotted and colored in!- Battleship game