Name:_________________________ Hour:______________ Date:________________
*2.5-Inverse Variation*
DIRECTIONS: Use the inverse variation formula y 
1. Use the formula y 
k
to solve the problems below.
x
k
to:
x
a) solve for k, if x= 12 and y= 5
b) solve for y, if x= 3 and k= 32
c) solve for k, if x= 3.4 and y= 2.2
d) solve for x, if y= 4.1 and k=20.5
2. Two quantities, x and y, are inversely proportional, when x=8, and y=4. Use these values and the
formula y 
k
to solve for the constant of variation (k).
x
a) When x=8 and y=4, k=?
y
x
b) Find the missing coordinates (x,y) for each point using the inverse proportion from part a.
I) (16, y)
II)
III) ( 0.2, y )
IV)
( x , 40)
( x, 12.8)
3. The amount of money in Harold’s savings account is inversely proportional to the number of bills he
has to pay each month. If x represents the number of bills he has to pay each month, and y represents
the money in his savings account, find the following:
a) Use the equation y 
k
to find k, the constant of variation; if Harold has $209 in his bank account,
x
when he has 3 bills to pay.
b) If Harold has 5 bills to pay this month, how much money will have in savings?
c) If Harold’s wife Sylvia sees only $69.67 in their savings account, about how many bills can she assume
they had to pay that month?
4. When Layla comes home from school she spends time either doing homework or sleeping. There
seems to be a relationship with between the two variables but her mom is not quite sure what kind it is.
Layla’s After School Schedule
Homework Time
2
3
4
6
8
12
12
8
6
4
3
2
(X)
(hours)
Sleeping Time
(Y)
(hours)
a) Does this data show a direct or inverse variation between Layla’s homework time and her sleeping
time? How do you know?
b) What is the constant of variation (k) in this problem?
c) Write an equation that represents the relationship of homework time (h) and sleeping time (s).
5. Circle whether each table or equation represents a direct variation or an inverse variation. Write the
constant of variation (k) for each problem.
a)
X
Y
3
12
b)
X
Y
1
3
c) y 
3
9
Direct or
Inverse
5
15
k=
4
9
Direct or
Inverse
6
6
k=
9
4
7
21
12
3
9
27
15
x
Direct or
Inverse
k=
d) y =12x
Direct or
Inverse
k=
6. a) How do we solve for the constant (k) in a direct variation problem?
b) How do we solve for the constant (k) in an inverse variation problem?