direct, inverse & joint variation. direct variation the variables x & y vary directly:...
TRANSCRIPT
Direct, Inverse & Joint Variation
Direct Variation
The variables x & y vary directly: ky
x
Direct Divide
ky
xBIGGER
BIGGER
Direct VariationThe variables x & y vary directly. Write an equation that relates x and y if x = 6 when y = 8. Then find x when y = 12.
ky
x
y
x
8
6
xy 86
68xy
xy 34
y
x
8
6
128
6 x
x8126
x872
x9
Inverse Variation
The variables x & y vary inversely: kyx Inverse Multiply
kyx BI
GG
ERSM
ALLE
R
Direct VariationThe variables x & y vary inversely. Write an equation that relates x and y if x = 3 when y = 12. Then find y when x = 9.
kyx yx123
xy36
yx123
y 9123
y936 y4
Determine whether x and y show direct variation, inverse variation, or neither.
x y
2 32
4 16
8 8
16 4
Direct Inverse
ky
x kyx
16
1
32
2
4
1
16
4
18
8
44
16
64322
64164
6488
64416
Determine whether x and y show direct variation, inverse variation, or neither.
x y
13 2
20 3
29 4
34 5
Direct Inverse
ky
x kyx
5.62
13
67.63
20
25.74
29
8.65
34
26213
60320
116429
170534
Determine whether x and y show direct variation, inverse variation, or neither.
x y
2 7
4 9
8 7
10 9
Direct Inverse
ky
x kyx
286.7
2
444.9
4
14.17
6
11.19
10
1472
3694
5678
90910
NEITHER
Joint Variation
The variable x varies jointly with y and z: k
zy
x
directly
Joint VariationThe variable z varies jointly with x & y. Write an equation that relates x, y, and z if x = 3, y = 7 and z = 8. Then find z when x = 9 and y = 4.
kyx
z
yx
z
738
4973
8
z
z21498
z21
498
z7
96yx
z
21
8
Write an equation for the relationship:
y varies directly with x and inversely with z.
kx
zy
Write an equation for the relationship:
a varies inversely with b and jointly with c and d.
kdc
ba
Write an equation for the relationship:
a varies directly with b and jointly with c and d.
kdcb
a