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Warm-Up Exercises
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Solve for a.
1. 10 5 2a 5
16
2. 5a 5 216 2}
5
3. Write an equation of the line
that passes through the points
(0, 0) and (4, 8). y 5 2x
4. A flower is 4.5 centimeters wide
and has a leaf 7.2 centimeters
long. What is the ratio of flower
width to leaf length? 5 to 8
Notetaking Guide
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Promotes interactive learning and
notetaking skills, pp. 40–42.
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Teaching Resources
For a complete list of lesson
resources, see page 64B.
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Pacing
%# Average: 1 day
Advanced: 1 day
Block: 0.5 block with 2.7
• See Teaching Guide/Lesson Plan
in Chapter 2 Resource Book,
pp. 59–60.
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(4, 7)
AND
2 FOCUS
MOTIVATE
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1 PREPARE
Essential Question
What is a constant of variation
and how is it related to slope? Tell
students they will learn how to
answer this question by studying
direct variation.
Starting the Lesson
1–4. See Additional Answers
beginning on p. AA1.
Have students let x be an arbitrary
number of servings of their favorite
item from the cafeteria. Then ask
them to use the cost per item to
write an equation to model the total
cost y of x servings.
101
3 TEACH
Extra Example 1
25
Graph y 5 }
x.
8
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(0, 0)
2
x
(8, 5)
Key Question to Ask
for Example 1
• How do you know the graph
contains the origin? If x 5 0 then
y 5 0, so (0, 0) is on the graph.
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Math Reasoning
Help students understand that they
y
can get the equation }x 5 k from a
direct variation equation by dividing
both sides of y 5 kx by x.
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Extra Example 2
A recipe for fruit punch uses 2
lemons to make 7 cups of punch.
Write an equation relating the
number of servings y to the number of
lemons x. How many cups of punch
can you make if you have 8 lemons?
y 5 }7x ; 56 cups of punch
2
Extra Example 3
An athlete ran 440 yards. Her coach
recorded the number of seconds x
and the number of yards y during
that run. Tell whether the data
show direct variation. If so, write an
equation relating x and y.
x
15
30
45
60
y
110
220
330
440
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• How does the value 30.3
relate to the Declaration of
Independence? There are about
30 words in each line.
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Key Question to Ask
for Example 3
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yes; y 5 1 7}1 2x
102
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