Download Class notes 10-28-2010

Section 3.1
Reading graphs and the Rectangular Coordinate System
Learning objectives
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Read bar & line graphs
Introduce the rectangular coordinate system
Graph paired data points on the rectangular coordinate
system
Graph points to create a scatter diagram
Find the missing coordinate of an ordered pair solution,
given one coordinate of the pair
Vocabulary: bar graph, broken line graph, ordered pair, origin,
quadrant, x-axis, y-axis, rectangular coordinate system,
coordinate plane, x-coordinate, y-coordinate, paired data,
scatter diagram
Example 1 – Reading bar & line graphs
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A bar graph is a series of
bars
They are used to compare
different quantities in
different categories
The quantity being
compared here is „number
of internet users‟
The category is region (ie.
US/Canada)
Which region has the
most internet users?
Worldwide Internet Users
4th Qtr
3rd Qtr
2nd Qtr
1st Qtr
Points
0
5
10
15
Series1
20
25
30
35
The graph shows points scored per quarter
for a basketball game
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Use the bar graph to find
the final score.
Take the readings from
each color for each
quarter and add them up
Celtics:
Lakers:
Points Per Quarter
35
30
25
20
15
10
5
0
1st Qtr
2nd Qtr
Celtics
3rd Qtr
Lakers
4th Qtr
Line graph
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A line graph consists of a
series of points connected
by a line.
This graph shows the
relationship between the
time spent smoking a
cigarette, and pulse rate
What point is the pulse
rate the highest?
The lowest?
Pulse rate
100
90
80
70
60
50
40
30
20
10
0
Time (minutes)
Pulse rate
Smoking pulse rate line graph
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What is the pulse rate 15
minutes after the cigarette
is lit?
Find the 15 along the
bottom
Then trace straight up
until you hit the line graph
The pulse rate at 15
minutes is 82 bpm
There is a point on the
graph with the ordered pair
of (15,82)
Pulse rate
100
90
80
82
70
60
50
40
30
20
10
0
-5 0 5 10 15 20 25 30 35 40
Monthly rent in Peru
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How much did monthly
rent increase in Peru
between 1980 and 2000?
What was monthly rent in
1990?
Was there a bigger change
between 1980 and 1990,
or between 1990 and
2000?
Monthly rent in Peru
1600
1400
1200
1000
800
600
400
200
0
1980
1990
2000
Ordered pairs of numbers
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We use the idea of ordered pairs of numbers to describe
the location of a point on a chart.
In math terms, the ordered pair represents a point on the
coordinate plane, just a fancy term for “on the chart”.
In math, the most commonly used type of coordinate
plane is the rectangular coordinate system
We have used number lines in the past. This shows points
going from left to right:
--|----|----|----|----|----|----|----|----|----|----|----|----|----|-
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
The rectangular coordinate system
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The rectangular
coordinate system is like a
number line going in two
directions.
The horizontal line is
called the x-axis
The vertical line is called
the y-axis
The two lines intersect at
the origin, also known as
the point (0,0)
Quadrants I, II, III, and IV
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The two axes, the x-axis and
the y-axis, divide the diagram
into 4 quadrants.
Anything in quadrant I has an
x-value greater than 0, as
well as a y-value greater than
0.
See the point P(3,5)?
This represents the point
where x = 3 and y = 5
The first number is always x,
and the 2nd always y
Since both are gt 0, P(3,5)
lies in Quadrant I
Rectangular coordinate system
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The point (0,0) is called
what?
It is the only point that
lies on both axes.
What quadrant would the
point (2,-5) fall in?
First, x=2. Start at the
origin, and go 2 spaces to
the right.
Then y=-5. Go 5 spaces
down.
You are in quadrant IV
Quadrants explained
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Quadrant I – x is positive,
y is positive. (3,5)
Quadrant II – x is negative,
y is positive. (-2,6)
Quadrant III – x is
negative, y is negative (-1,2
Quadrant IV – x is
positive, y is negative
Quadrants exercise
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Each ordered pair
represents 1 point on the
graph. (3,5) is one point
in quadrant I
Which quadrant is (-2,5)?
(0,-4)
(2.6, 4.5)
(-1, 4)
Scatter diagrams
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Each ordered pair
represents exactly one
point on the plane
Data that can be
represented as ordered
pairs are called paired data
A plot of paired data
points on a rectangular
diagram is called a scatter
plot
Example of paired data: a
child‟s height by age
Y-Values
4
3
2
1
0
-5
-1 0
-2
-3
-4
-5
5
Example 4 – Target net sales
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In 1999, net sales was 34
billion, and 2000 was 37.
We can pair these values
with x = year and y =
billions
(1999,34) (2000,37)
(2001,40) (2002,44) and
(2003,48)
The x-axis shows the years
along the bottom
The points represent the net
sales amounts in billions
Net Sales (billions)
50
45
40
35
30
25
20
15
10
5
0
1998
2000
2002
2004
Scatter diagram exercise
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Bookstore sales by year:
2000 – 19 thousand
2001 – 22 thousand
2002 – 21 thousand
2003 – 23 thousand
2004 – 25 thousand
2005 – 26 thousand
Write the ordered pairs
Create a scatter diagram
with these ordered pairs
Completing ordered pair solutions
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We can use ordered pairs to record solutions of
equations containing TWO variables
The equation x + 3 = 6 has only one solution: x = 3
How about the equation 2x + y = 8?
These two-variable equations have solutions consisting of
two values, one for x and one for y
We can replace x with 3 and y with 2. This is a solution
to our equation, and it is written as an ordered pair: (3, 2)
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
Completing ordered pair solutions, cont
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However, there can be more than one ordered pair as a
solution.
Generally, if we give you one number in the pair, substitute it
into the equation to find the other number
Complete each ordered pair as a solution for 3x + y = 12
(0, )( ,6)
(-1, )
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First, (0, ) : 3(0) + y = 12;
0 + y = 12; y=12; (0,12)
( ,6): 3x + 6 = 12; 3x = 6; x = 2;
(2,6)
(-1, ): 3(-1) + y = 12;
y = 15;
(-1, 15)
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The ordered pairs (0,12), (2,6), and (-1,15) are all solutions
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Complete each ordered pair so that it is a
solution of the given linear equation
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x + 2y = 6;
(2,
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y = 1/3 x – 2;
(6, )
( , -3)
(
,-1/3)