2-2 reteaching - orange county public...
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Prentice Hall Algebra 2 • Teaching ResourcesCopyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
19
Name Class Date
A direct variation is a function of the form,
y 5 kx or yx 5 k, where k 2 0.
Represent the input values as x and represent the output values as y. ! e ratio of
any output-input pair is equal to k, the constant of variation.
Problem
For each function, determine whether y varies directly with x. If so, what is the
constant of variation?
Exercises
For each function, determine whether y varies directly with x. If so, ! nd the
constant of variation.
1. 2. 3.
4. y 5 4x 1 1 5. 5y 5 24x 6. 3y 1 4x 5 0
7. 2y 5 4x 2 5 8. 3y 5 15x 9. 34y 2 17x 5 0
x y
22
23
24
4
6
8
x y
4
6
8
1
2
3
x y
3
9
12
6
18
24
2-2 Reteaching
Direct Variation
Identify direct variation from a table. Identify direct variation from an equation
a.
Find y
x for each ordered pair.
This is a direct variation. The constant of
variation is 3
2
5
9
6
3
2,
12
8 5
3
2,
15
10 5
3
2
. So, k 5
3
2.
b. 2y 5 5x 2 3
Try to put the equation in the form y 5 kx.
This is not a direct variation because there is aconstant left when you try to put it in the formy 5 kx.
x y
6
8
10
9
12
152y 5 5x 2 3
2 2 2Divide both sides by 2.
2y 5x5 2
3
Simplify.2 2
5y 5 x 2
3
yes; 2 no yes; 22
no
no yes; 5
yes; 2 45 yes; 2
43
yes; 12
Prentice Hall Algebra 2 • Teaching ResourcesCopyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
20
Name Class Date
If you know that y varies directly with x and you are given one set of values, you
can use the equation for direct variation to " nd other sets of values.
Problem
What is the missing value in each direct variation?
a. If y 5 5 when x 5 2, " nd y when x 5 7.
k 5yx 5
52 Use y 5 5, x 5 2, and k 5
yx to fi nd the value of k.
y 552 x Now use the form y 5 kx and k 5
52
to write the equation of the direct variation.
y 552 x 5
52 (7) 5
352 5 17
12 To fi nd the value of y when x 5 7, replace x with 7 in the direct
variation equation and simplify to fi nd y .
b. If y 5 6 when x 5 23, " nd x when y 5 24.
k 5yx 5
623 5 22 Use y 5 6, x 5 23, and k 5
yx to fi nd the value of k.
y 5 22x Now use the form y 5 kx and k 5 22 to write the equation of the direct variation.
24 5 22x To fi nd the value of x when x 5 24, replace y with 24 in the
2 5 x direct variation equation and solve for x .
Exercises
Find the missing value for each direct variation.
10. If y 5 8 when x 5 4, " nd y when x 5 6. 11. If y 5 12 when x 5 3, " nd y when x 5 5.
12. If y 5 9 when x 5 3, " nd x when y 5 7. 13. If y 5 26 when x 5 2, " nd x when y 5 9.
14. If y 5 32 when x 5
14, " nd y when x 5
23. 15. If y 5 7 when x 5 2, " nd x when y 5 3.
16. ! e height of an object varies directly with the length of its shadow. A person
6 ft tall casts an 8
12 ft shadow, while a tree casts a 38 ft shadow. How tall is
the tree?
2-2 Reteaching (continued)
Direct Variation
67
26
1417 ft
12
73
20
23
4