2-2
Direct Variation
Vocabulary
Review
1. Cross out the ratio that is NOT equal to the others.
3.5
1
7
2
10.5
3
9
4
Solve each proportion.
3
9
x
16
2. 2 5 x
3. 3 5 12
x5
x5
x
5
4. 2 5 7
x
5. 29 5 18
x5
x5
direct (adjective) duh REKT
Other Word Forms: directly (adverb), directions (plural noun)
Main Idea: Direct describes two quantities that vary in the same way: increasing
together or decreasing together.
Definition: Something that is direct is proceeding from one point to another,
in time or space, without interruption.
Use Your Vocabulary
Choose the correct word from the list to complete each sentence.
directly
direct
directions
6. Tomás gave the visitor 9 to the stadium.
7. The fans went 9 to their seats.
8. There was a 9 connection between the team’s
scoring and the fans’ cheering.
Chapter 2
30
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Vocabulary Builder
Problem 1 Identifying Direct Variation From Tables
Got It? For the table at the right, determine whether y varies directly with x.
If so, what are the constant of variation and the function rule?
9. Write the ratio of the input-output pairs in simplest form.
Input-Output Pair
(3, 21)
21
3
Ratio
(2, 14)
(1, 7)
2
1
x
2
3
y 21 14 7
10. Underline the correct word(s) to complete the sentence.
y
Since the ratio x is / is not the same for all of the input-output pairs,
the function is / is not a direct variation.
11. If possible, identify the constant of variation and write a function rule.
k5
y5
x
Problem 2 Identifying Direct Variation From Equations
Got It? For the function 5x 1 3y 5 0, determine whether y varies directly with x.
If so, what is the constant of variation?
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
12. Solve the equation for y.
13. Circle the constant of variation.
5
23
3
5
5
3
None
Problem 3 Using a Proportion to Solve a Direct Variation
Got It? Suppose y varies directly with x, and y 5 15 when x 5 3.
What is y when x 5 12?
15. Simplify the proportion you wrote in Exercise 14.
14. Complete the proportion below.
5
y
16. When x 5 12, the value of y is
.
31
Lesson 2-2
Problem 4
Using a Proportion to Solve a Problem
Got It? The number of Calories varies directly with the mass of cheese. If 50 grams
of cheese contain 200 Calories, how many Calories are in 70 grams of cheese?
17. Complete the model below. Let c 5 Calories.
Relate
the ratio of
the ratio of
200 Calories to
c Calories to
is the same as
50 grams
70 grams
200
Write
18. Solve the proportion for c.
19. There are about
Graphing Direct Variation Equations
Got It? What is the graph of the direct variation equation y 5 2 23 x?
20. Complete the table.
x
3
3
0
y
21. Graph the direct variation.
4
3
2
1
4 3 2 1 O
1
2
3
4
Chapter 2
y
x
1 2 3 4
32
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Problem 5
Calories in 70 grams of cheese.
Lesson Check • Do you UNDERSTAND?
Reasoning Explain why the graph of a direct variation function always passes
through the origin.
22. Write direct variation if the graph is a direct variation. Write linear if the
graph is a linear function that is not a direct variation.
y
y
2
2
O
y
2
2
x
x
2
2
2
2
2
2
O
x
2
2
23. Write D if the equation describes a direct variation. Write L if the equation
describes a linear function that is not a direct variation.
y 5 22x
y5x
y 5 2x 1 2
24. Circle the true statement.
A linear function is always a direct variation.
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25. Write the direct variation equation of a
function with constant of variation k.
A direct variation is always a linear function.
26. Evaluate the function you wrote in
Exercise 25 for x 5 0.
27. Why does the graph of a direct variation function always pass through the origin?
_______________________________________________________________________
Math Success
Check off the vocabulary words that you understand.
direct variation
constant of variation
Rate how well you can identify and use direct variation functions.
Need to
review
0
2
4
6
8
Now I
get it!
10
33
Lesson 2-2