
Translate the following phrases.
1. fifty less than 2 times x 𝟐𝒙 − 𝟓𝟎
𝟔
2. the quotient of 6 and y, increased by one + 𝟏
𝒚
3. the product of z and five more than z 𝐳(𝒛 + 𝟓)
List the characteristics of Direct
proportion/variation.
Formula: y=kx
y
x
Graph: Straight line that goes through origin
Formula for k: k 
X & Y Relationship: They move in the same
direction – up together
or down together.
List the characteristics of
Inverse proportion/variation.
k
Formula: y 
x
Formula for k: k=yx
Graph: The line curves & will never
touch the x or y axis.
X & Y Relationship: They move different
directions.
3. When you are given a table of values for x
and y, how can you tell if it represents a
direct, an inverse proportion (variation) or
neither?
Look to see if you can find a constant.
AND
If the variables have a relationship.
4. Looking at the following table of values
k=yx
X 1 2 3 6
Y 6 3 2 1
6 6 6
6
Do the points represent a direct
proportion (variation), inverse
proportion (variation), or neither?
Inverse
5. What is the constant of variation in the
following table?
y
k
x
X
8
6
5 12
Y
64 48 40 96
8 8 8
8
Example
of Direct
40
6. What type of proportion (variation) is y 
?
x
Inverse
What is the constant?
40
7. What type of proportion (variation) is y  6 x ?
Direct
What is the constant?
6
8. If y varies inversely with x, and y=6 and x=7,
what is the rule (equation) for this proportion
(variation)?
k
k Multiply both
y
6  sides by 7
x
7
k = 42
42
y
x
9. If x varies inversely with y. If x=8 when y=2,
what is the value of y when x=4?
k Multiply both
k
16
2
y
y
x
8 sides by 8
k = 16
4
y=4
10. If y=15 and x=6, using an inverse
proportion (variation), what is the value of y
when x=18?
Multiply
k
k
y
15 
both sides
x
6
by 6
k = 90
90
y
18
y=5
11. If y varies directly with x, and y=4 and x=36,
what is the rule (equation) for this proportion
(variation)?
y  kx
4  36k Divide both
4
36k sides by 36

36
36
1
k
9
1
y x
9
12. If y varies directly with x. If y=6 and x=2,
what is the value of y when x=5?
y  kx 6  2k
6 2k

2
2
k 3
Divide both
sides by 2
y  35
y  15
13. If y varies directly with x. If y=21 and x=42,
what is the value of y when x=52?
y  kx 21  42k Divide both
21 42k

42
42
1
k
2
sides by 42
OR k = .5
y  .5  52
y  26
14. Sandra uses
1
22
cups of sugar to bake
6 dozen chocolate chip cookies. How many
cups of sugar would she need to bake
10 dozen cookies?
cups
dozen
2.5 x

6 10
6 x  25 Divide both
1
x4
6
sides by 6
15. Alex rides his bike from school to home in
x
y
30 minutes traveling 20mph. Today he needs
to get home 5 minutes faster. How fast must
he ride his bike?
k
y
x
600
y
25
k Multiply
20 
both sides
30 by 30
y  24mph
600  k
16. The product of the number of i-tunes and
video-casts purchased is 32. If 16 video-casts
are purchased how many i-tunes can be bought?
y  kx
32  16x Divide both
2x
sides by 16
17. The number of pages Jimbo can read varies
directly with the time he spends reading. If
he reads 10 pages in 30 minutes, how many
pages can he read in 120 minutes?
10
x 30 x  1200 Divide

both
mins 30
120
sides by
pages
x  40
pages
30

Tomorrow I will have tutoring at 8:15 am.
Come in if you would like some more practice
with me before your test.
 Study,
Study, Study…