-
Date:
Homework #35: Direct Variation
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IDENTIFYING DIRECT VARIATION EQUATIONS: Tell whether the equation represents direct
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variation . If so, identify the constant of variation.
1) y =
WUJ
x
0- -:::..-\
·-. --y.
\
2) y = 5x - 1
N\D
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=3
x- 3y =0
S"D'D
( b -:;. 3 )
3) 2x + y
4)
Q._-=-l/~
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B) 3x -
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)
c_
6) Which equation is a direct variation equation?
A) y = 7 - 3x
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ran
5) 2.4x + 6 = 1.2y
J
7y = 1
€3x-7y= 0
D) 3y = 7x - 1
7) ERROR ANALYSIS: Describe and correct the error in identifying the constant of variation
for the direct variation equation -5x + 3y 0.
-5x + 3y = 0
=
~=...5x-
Ti?e
c~nstant of variation
is 5.
Q... :;.
.s...
'j=!x
Write the direct variation equation. Then find y when x = 8 .
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WRITING EQUATIONS: Given that yvaries directly with x, use the specified values to write a
direct variation equation that relates x and y.
12) x = 3, y = 9
j-::.. o....x
C\ -=·- ~·~
a_'"::-~
14) x = 15, y = -5
~ =.CAX
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= 14, y =7
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13) x
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v- --x
.3
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----==::: \S \5 -
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j
=--
-3
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llt
15) x = -6, y = 15
l
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2,...
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16) The distanced (in meters) you travel on a bicycle varies directly with the number rot
revolutions that the rear tire completes. You travel about 2 meters on a mountain bijke for
every revolution of the tire.
d ~ ~ '(""
a) Write a direct variation equation that relates rand d.
d-:::.- '3DC()'f'f\
d-=- ~( \SDD\
b) How many meters do you travel in 1500 tire revolutions?
d -=.
tA, • '{
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o....-:-t-
17) At one company, the amount of vacation time v (in hours) varies directly with them amount
of time t (in weeks) he or she works. An employee who works 2 weeks earns 3 hours of ...Lvacation .
(A;,~
2,h&~ -=-°'-A~
How many hours of vacation time does an employee earn in 8 weeks? Q b''A.l
a) Write a direct variation equation that relates tand
b)
v-::...
v.
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j =- \. ,____,
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7:.-
neeaea aepenas on me aepm a
stone that is 2 inches deep.
~m
mcnesJ or me 1ayer. 1ney neea ·1 u oags to spreaa a 1ayer or
.3 -:oO.,.d.
S : :. S ~
a) Write a direct variation equation that relates d ands.
II)
b) How many bags of stone is needed to spread a layer that is 3 inches deep?
S :.. \5 ~5
S-=:-5. 3
°'- ~ 5
~-=-o.__w
~At a recycling ·center, computers and computer accessories can be
recycled for a fee f based on the weight w, as shown in the table.
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a) Write a direct variation equation that relates f and w.
~%Qt>~
4-w
d--\
b) What is the.total recycling fee for a computer that weighs
18 pounds and a printer that weighs 10 pounds.
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Weight, w
(poupds)
Fee, f
(dollars)
10
15
30
2.50
3.75
7.50
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Q~L\-
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20) You can buy gold chain by the inch. The table shows the price of gold chain for various
p-=-
lengths.
7
8.75
Q
~
I9
I 16
I 18
I 11.25
I 20.00
I 22.50
. 5&·15-=-0"l
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cy ? \.d..SY
If you have $30, what is the longest chain that you can buy? 167" 56
a) Write a direct variation equation that relates I and p.
b)
1' ~ ~(t.dS)
~
~
0 A W=6L
•
\N ::o-o. L
B. W =3L
0 C_ L = 3W
0 Q _ L""9W
lo ::
~· d.
3 :::::.°'-..
w-=-3L
Write the variation and find the quantity indicated x varies directly withy. If xis
54 wheny is 100. find.:r wheny is 200.
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~
O A 1080
0 B_ Tl
i!J C. 108
0 0 - 370~
27
x~~j (-r_~~54~D.' ltt>
----\,Cb
______.
\tD
()_::::. 54
----
7
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X=~(~
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x-=- \C)i
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