Download 4.1 Lesson

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
EXAMPLE 1
Name points in a coordinate plane
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 2
Plot 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 3
Graph a function
Graph the function y = 2x – 1 with domain –2, –1, 0, 1,
and 2. Then identify the range of the function.
SOLUTION STEP 1 Make a table by substituting the
domain values into the function.
STEP 2
List the ordered pairs:
(–2, –5), (–1, –3), (0, –1), (1, 1), (2, 3).
Then graph the function.
STEP 3
Identify 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 the
location of the point.
1. A(2, 5)
ANSWER
2.
Quadrant I
B(–1, 0)
ANSWER
3.
C(– 2, –1)
ANSWER
4.
x-axis
Quadrant III
D(–5, 3)
ANSWER
Quadrant II
GUIDED PRACTICE
for Examples 2 and 3
Plot the point in a coordinate plane. Describe the
location of the point.
1
5. Graph the function y = – 3 x + 2 with domain –6, –3,
0, 3, and 6. Then identify the range of the function.
ANSWER
range: 0, 1, 2, 3, and 4
EXAMPLE 4
Graph a function represented by a table
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.
Years before or
since 1920
–12
–8
–4
0
4
8
12
Votes (millions)
15
15
19
27
29
37
40
a.
b.
c.
Explain how you know that the table represents a
function.
Graph the function represented by the table.
Describe any trend in the number of votes cast.
EXAMPLE 4
Graph a function represented by a table
SOLUTION
a. The table represents a function because
each input has exactly one output.
b. 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).
The graph of the function is shown.
c. 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.
GUIDED PRACTICE
for Example 4
VOTING
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.
–12 –8
–4
0
4
8
12
Years before or
since 1972
Votes (millions)
a.
69
71
73
78
82
87
93
Explain how you know the graph represents a
function.
ANSWER The table represents a function because each
input has exactly one output.
GUIDED PRACTICE
for Example 4
b. Graph the function represented by the table.
ANSWER
c.
Describe any trend in the number of votes cast.
ANSWER 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.
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 coordinate
plane 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