Study Island Assignment #6 Warm-ups
Name ________________________________ Per ___
Topic #2 – Linear Relationships
1. A study was done to investigate the use of text messaging over time. The correlating linear model
is shown below, where x represents the number of years after 2006, and y represents the
number of text messages the average person sends monthly.
Interpret the y-intercept:
y = 146x + 65
A.
B.
C.
D.
In 2005, the average person sent 146 text messages per month.
In 2005, the average person sent 65 text messages per month.
In 2006, the average person sent 65 text messages per month.
In 2006, the average person sent 146 text messages per month.
2. Brandon has a 55-gallon fish tank. He estimates he can drain the tank at an average rate of
11 gallons per minute. In a linear model of this situation, x represents the number of minutes
the tank has been draining. Relative to this situation, what does the y-intercept represent?
A.
B.
C.
D.
The y-intercept represents the amount of water in the tank after it has been drained.
The y-intercept represents the amount of water in the tank before it has been drained.
The y-intercept represents the number of minutes it takes to drain the tank.
The y-intercept represents the rate at which the tank can be drained.
3. Edmond is on the third day of his hike up Glacier Peak. The graph below shows his hiking time and
altitude for that day only.
What was his altitude at the beginning of the third day?
A.
B.
C.
D.
2,000 feet
2,500 feet
3,000 feet
5,500 feet
4. The graph shows the cost of a taxi in New York City.
What is the rate of change of the graph?
A.
B.
C.
D.
$2.00 per mile
$2.50 per mile
$4.00 per mile
$1.00 per mile
5. A group of friends is going to an amusement park over the weekend. The table below shows the
total cost in relation to the number of friends who are going to the park.
No. of Friends
2
3
4
5
6
Total Cost
$40.00 $60.00 $80.00 $100.00 $120.00
What is the rate of change for the information in the table?
A. $10.00 per person
B. $20.00 per person
C. $40.00 per person
D. $30.00 per person
6. Rick buys and sells antiques via the Internet. So far, he has profited $2,502. Based on his profits
to date, he developed the following linear model where x represents time in months, and y
represents his total profits (in dollars). Interpret the slope:
y = 2,502 + 417x
A.
B.
C.
D.
An additional month of buying and selling is associated with an additional $2,502 in profits.
An additional month of buying and selling is associated with an additional $417 in profits.
An additional month of buying and selling is associated with an additional $2,085 in profits.
An additional month of buying and selling is associated with an additional $2,919 in profits.
7. A bowling alley charges its customers an hourly rate to bowl plus shoe rental. The hourly rates are
per lane. A linear model of this situation contains the values (3, 57.25) and (4, 75.5),
where x represents the number of hours bowled on one lane, and y represents the total cost
for bowling. What is the rate of change in this linear model?
A. $54.75 per hour
B. $18.25 per hour
C. $2.50 per hour
D. $9.12 per hour
8. Julie bought a drink for $2.99, two bags of chips for $1.29 each, and some gasoline at a
convenience store. The price of gasoline was $2.99 per gallon. If x represents the number of
gallons of gasoline she purchased, which of the following equations can be used to find how
much Julie spent at the convenience store?
A.
B.
C.
D.
y = 4.28x + 2.99
y = 2.99x + 4.28
y = 2.99x + 5.57
y = 5.57x + 2.99
9. On average, Matt’s Manufacturing Company produces 130 units in five working days and
650 units in twenty-five working days. In a linear model of this situation, which of the
following statements applies?
A.
B.
C.
D.
An additional day of production is associated with an additional 104 units.
An additional day of production is associated with an additional 7.8 units.
An additional day of production is associated with an additional 26 units.
An additional day of production is associated with an additional 39 units.
10. Helen has been working on a science project about plant growth. Plant A started at a height of
6 cm and exhibited steady growth during the first four weeks of the project. After those four
weeks, Plant A was 26.8 cm in height. In a linear model of Plant A’s growth, x represents the
number of weeks after being planted, and y represents the plant’s height (in cm). Relative to
this model, which of the following statements applies?
A.
B.
C.
D.
An additional week of growth is associated with an additional 8.2 cm of plant height.
An additional 8.2 weeks of growth is associated with an additional cm of plant height.
An additional 5.2 weeks of growth is associated with an additional cm of plant height.
An additional week of growth is associated with an additional 5.2 cm of plant height.
11. Jaren is the manager of a department store. The morning of a big holiday sale, when Jaren
opened the door, 12 customers were waiting outside to come into the store. Each hour the
store is open, another 13 customers enter the store, and 8 customers leave the store.
Use this information to complete the table.
The x-values represent the number of hours the store is open.
The y-values represent the number of customers in the store.
The equation which represents the number of customers in the store
is y =
x+
Hours
Open
Number of
Customers
in the Store
0
12
1
17
2
22
3
4
12. A data analyst for a phone company is analyzing the data of 150 of their customers, which
accounts for 1% of their total customers. The analyst wants to determine the average number
of hours each day a customer uses his/her phone, for calls and for texts, during a 30-day
period. Based on the data, the customers averaged 0.25 hours per day per call and 1.75 hours
each day for texts. Construct an equation in the correct form to represent this situation. Let t
represent the number of calls made per day and e represent the total number of hours a
customer uses his/her phone each day.
1.75
e=
0.01
t
+
150
30
1
0.25