Transcript 12-5 Direct Variation

12.5 – 12.7
Variation
CA Standard 15.0
Apply algebraic techniques to rate
problems.
Vocabulary
 Direct Variation
y  kx
Constant of Variation
#1 Find an equation of variation where
y varies directly as x.
y  84 when x  12
y  kx
84  12 k
k 7
y  7x
#2 Find an equation of variation where
y varies directly as x.
y  50 when x  80
y  kx
50  80 k
k  0.625
y  0.625x
Vocabulary

Inverse Variation
k
y
x
#3 Find an equation of variation
where y varies inversely as x.
y  105 when x  0.6
k
y
x
k
105 
0. 6
63
k  63
y
x
#4 Find an equation of variation
where y varies inversely as x.
y  45 when x  20
k
y
x
k
45 
20
900
k  900
y
x
#5 Solve the problem using direct
variation.
 The Weight (V) of an object on Venus varies
directly as its weight (E) on Earth. A person
weighing 120 lb on Earth would weigh 106 lb
on Venus. How much would a person
weighing 150 lb on Earth weigh on Venus?
V  106 lb
E  120 lb
#5 Solve the problem using direct
variation.
V varies directly with E
Find an equation Solve for V when E is 150
V  kE
V  0.88 E
106  120 k
V  0.88(150)
k  0.88
V  132 lb
V  0.88 E
#6 Solve the problem using inverse
variation.

The time (t) required to drive a fixed
distance varies inversely as the speed
(r). It takes 5 hours at 60 km/h to drive a
fixed distance. How long would it take to
drive the same distance at 40 km/h?
t  5 hours
r  60 km/h
#6 Solve the problem using direct
variation.
t varies inverselywith r
Find an equation Solve for t when r is 40
k
t
r
k
5
60
k  300
300
t
r
300
t
r
300
t
40
t  7.5 hours
Vocabulary
• Joint Variation
z  kxy
#7 Find an equation of variation where
w varies jointly as x, y, and z.
w  36, x  3, y  5, and z  6
w  kxyz
36  3(5)(6)k
36  90 k
2
k
5
2
w  xyz
5
#8 Find an equation of variation where
Q varies jointly as R and S.
Q  2, R  1, and S  3
Q  kRS
2  1(3)k
2  3k
2
k
3
2
Q  RS
3
Vocabulary
• Combined Variation
kx
z
y
#9 Find an equation of combined variation
where P varies directly as q and inversely as r.
P  0.064, q  16, and r  5
kq
P
r
16 k
0.064 
5
0.32  16 k
k  0.02
0.02 q
P
r
#10 Solve the problem using
combined variation.
• Find an equation of combined
variation where A varies directly as b
and inversely as c. One set of values
is A = 4, b = 12, and c = 9. Find A
when b = 7 and c = 3.
kb
A
c
#10 Solve the problem using
combined variation.
A  4, b  12, and c  9
12 k
Find A when b  7 and c  3
4
9
3(7)
A
36  12 k
3
k 3
21
A
3b
3
A
c
A7
#11 Solve the problem using
variation.
• The interest earned at Whole World
Savings & Loan varies jointly as the
amount deposited in the bank and
the time elapsed since the deposit.
If a $500 deposit earns $120 interest
after 3 years, how much does an
$800 deposit earn after 5 years?
I  $120
D  $500
t  3 years
#11 Solve the problem using
variation.
I varies jointly with D and t
Find an equation $800deposit after5 years
I  kDt
I  0.08(800)(5)
120 500(3)k
I  0.08(4000)
120  1500 k
k  0.08
I  0.08 Dt
I  $320