Transcript BEI06_ppt_0301

Chapter 3
Introduction to
Graphing
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3.1
Reading Graphs, Plotting Points, and
Scaling Graphs
• Problem Solving with Bar, Circle, and Line
Graphs
• Points and Ordered Pairs
• Numbering the Axes Appropriately
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Bar Graphs
A bar graph is a convenient way of showing
comparisons. In every bar graph certain
categories, such as level of education in the
example, are paired with certain numbers.
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Example
The bar graph shows the median weekly earnings
for full-time wage and salary workers ages 25 and
older. Estimate by how much the median weekly
earnings of a high school graduate exceeds that
of a person who did not earn a high school
diploma.
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Example
We locate “high school graduate” and go to the top
of that bar. Then we move horizontally from the top
of the bar to the vertical scale, which shows
earnings. We read there about $600.
Next repeat for “less than high school”, we read
about $400.
$600 – $400 = $200
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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.
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Points and Ordered Pairs continued
To plot the point (2, 3)
we start at the origin,
move horizontally to
the 2, move up
vertically 3 units, and
then make a “dot”.
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(2, 3)
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Example
Plot the point (4, 3).
Solution
Starting at the origin,
we move 4 units in the
negative horizontal
direction (left). The
second number, 3, is
positive, so we move 3
units in the positive
vertical direction (up).
(–4, 3)
3 units up
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4 units left
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Example
Find the coordinates of points A, B,
C, D, E, F, and G.
Solution
A: (5, 3)
B: (2, 4)
C: (3, 4)
D: (3, 2)
E: (2, 3)
F: (3, 0)
G: (0, 2)
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B
A
E
G
F
D
C
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Quadrants
The horizontal and vertical axes divide the
plane into four regions, or quadrants.
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Numbering the Axes Appropriately
Often it is necessary to graph a range of x-values
and /or y-values that is too large to be displayed if
each square of the grid is one unit wide and one
unit high.
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Example
Use a grid 10 square wide and 10 squares high to
plot (24, 460) and (38, 85) and (10, 170).
Solution The x-values range from a low of 24 to a
high of 38. The span is 38  (24) = 62 units
Because 62 is not a multiple of 10, we round up to
the next multiple of 10, which is 70. Dividing 70 by
10 we would have a scale of 7 which is not
convenient so we round up to 10.
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Example
The y-values span from 170 to 460, the vertical
squares must span from 460  (170) = 630. For
convenience, we round 630 up to 700, and then
divide 700 by 10 = 70. Using 70 as the scale.
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Example
Combine the work from
the x and y-values to
create the grid and plot
the points.
(24, 460) and (38, 85)
and (10, 170).
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