Name ________________________________________ Date __________________ Class __________________
Inverse Variation
LESSON
9-1
Reteach
y varies directly as x
y varies inversely as x
k
y=
x
y = kx
k=
k = xy
Decide if the data in the table shows direct or
inverse variation. Write an equation that relates
the variables.
Example
1. if
y
x
y
is constant → direct variation
x
if xy is constant → inverse variation
x
3.1
5.4
8.7 10.6
y
9.3
16.2 26.1 31.8
y
= 3 for all pairs, so it is direct variation.
x
2. Find k.
Since,
3. Write the equation.
y = 3x
y
= 3, k = 3.
x
Decide if the data in the table shows direct or inverse variation. Write
an equation that relates the variables.
1.
x
2.5
y
4
8
16
2.
1.25 0.625
________________________
x
−2
3
10
y
6
−4
−1.2
_______________________
3.
x
2.8
3.2
5.9
y
25.2
28.8
53.1
__________________________
Example If x varies inversely as y and x = 4 when y = 12, find y when x = 6.
1. Substitute the values for x and y.
2. Solve for k.
3. Substitute for k.
k
x
k
12 =
4
48 = k
y=
48
x
48
y=
6
y =8
y=
4. Substitute for x.
5. Solve for y.
4. If y varies inversely as x and y = 2 when
x = 20, find y when x = 8.
5. If y varies inversely as x and y = 0.4 when
x = 5, find y when x = 4.
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