Directions: Team Exploration 11.1
Identify Direct Variation and Inverse Variation
1. Title the notes in your spiral notebook, “Notes 11.1 Direct and Inverse
Variation”
2. Complete Activity 11.1A : Copy the flowchart and work the activity cards
(examples 1-3) in your spiral. Check your answers before moving on!
3. Write the new topic title in your notes: “How to find “k” , model equation
and/or a missing value) if you are given the type of variation”.
(flowchart 11.1B will show how to do this)
4. Complete Activity 11.1B : Copy the flowchart and work the activity cards
(examples 4-6) in your spiral. Check your answers before moving on!
5. Copy Activity 11.1C : Copy the notes and work the activity card
(examples 7-8) into your spiral. Check your answer before moving on!
6. Complete HW Puzzle 11.1 and the problems below in your spiral - for
homework.
HW 11.1
20. Gravitational potential energy is a measure of energy. PE varies jointly
with an object’s mass m and its height h in meters above the ground.
Physicists use g to represent the constant of variation, which is gravity. A
skateboarder on a half-pipe has a mass of 58kg and a potential energy of
2273.6 joules. What is the gravitational potential energy of a 65-kg
skateboarder on the same 4m high half-pipe?
21. The number of buckets of paint n needed to paint a fence varies directly
with the total area a of the fence and inversely with the amount of paint p
in a bucket. It takes three 1-gallon buckets of paint to paint 72 sq. ft. of
fence. How many 1-gallon buckets will be needed to paint 90 sq. ft. of
fence?

Activity 11.1B
Given the type of Variation and a given ordered pair, find missing parts or the model of variation
The Variation of Proportionality is:
Substitute the Values of the x (independent variable ) and y (Dependent Variable ) into 𝒚 𝒌 = 𝒙 to find k to find k
Substitute the Value of “k” and the given x or y value into 𝒚 𝒌 = 𝒙 to find the other missing value
Substitute the Values of the x (independent variable) and y (Dependent Variable) into k=xy
Substitute the Value of “k” and the given x or y value into k=xy to find the other missing value

Activity 11.1 C
Notes: Using Combined Variation
Using Combined Variation
How can you write the combined variation model ?
 Y= (or dependent variable of choice) … (z varies means z = )
 Put “ k ” (constant of variation) in the numerator.
 Write variable(s) representing direct variation in the numerator .
 Joint variation means multiply multiple things in direct var.
(in numerator)
 Write variable(s) representing inverse variation in the denominator
When describing a combined variation – the “k” is not in the description
Example:
The number of bags of grass seed n needed to reseed a yard varies directly with the area a to be seeded and inversely with the weight w of a bag of seed.
If it takes two 3-lb bags to seed an area of 3600 sq. ft., how many 3-lb. bags will seed 9000 sq. ft.?
Steps:
1. Write the variation model equation: 𝒏 = 𝒌𝒂 𝒘
𝒐𝒓 𝒌 𝒂 𝒘
2. Sub the given data to find “k” 𝟐 =
𝟑𝟔𝟎𝟎𝒌
𝟑
3. Solve for k:
(𝟐)(𝟑)
𝟑𝟔𝟎𝟎
= 𝒌
4. Simplify to find k: 𝒌 =
𝟏
𝟔𝟎𝟎
5. Replace k in original model equation : 𝒏 =
𝟏
𝟔𝟎𝟎 𝒂
( 𝒘
) or 𝒏 = 𝒂
𝟔𝟎𝟎𝒘
6. Sub info into model equation to solve for unknown: n

1
600 n

5
9000
3 bags

11.1A Activity Card Ex. 1
Do the data in the table represent a direct variation or inverse variation?
Find the constant of variation (k) .
X 4 3 2 1 y 12 9 6 3
(3,
11.1B Activity Card Ex. 4
1
2
) is a coordinate from an inverse variation.
A.
Find the constant of variation
B.
Find the model equation for this inverse variation.
11.1A Activity Card Ex. 2
Do the data in the table
3 represent a direct vari ation or inverse variation? Find the constant of variation (k) . x y
3
1.5
4
2
5
2.5
6
3 variation? Find the constant of variation (k) x y
11.1A Activity Card
1
24
2
12
Ex. 3
8
4
6
11.1B Activity Card Ex. 5 𝑥 =
−3 when 𝑦 =
2 and
10 9 they vary inversely.
A.
Find the constant of variation
B.
Find the model equation for this variation.
11.1B Activity Card Ex. 6
Each pair of values is from a direct variation.
Find the missing value.
(3 , 18) , (x , 27)
11.1C Activity Card Ex. 7
The time t needed to complete a task varies inversely as the number of people p. It takes
5h for seven men to install a new roof. How long does it take ten men to complete the job?
11.1C Activity Card Ex. 8
Z varies directly with x and inversely with y. Write an equation for this. When x=6 and y=2, z = 15. Find k. Replace k in your model equation you wrote. Find z when x=4 and y=8.

Does this data represent
,
, or
? y
 kx thus k
 y x y
 k x thus k
 xy