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Constructing Linear Functions

Terms in this set (16)

Myles is tracking the growth of his palm tree. It was 62 inches when he bought it, and it has grown 6 inches per year.
What does the initial value represent?
Answer: ✔ The height the tree was when bought.

What is the input for the initial value?
Answer: ✔0

What is the output for the initial value?
Answer: ✔62
The table to the right displays the weight progress of a puppy at the end of week 4. If the relationship between time and weight is linear, how much did the puppy weigh at birth?
Answer: ✔6 pounds
An indoor trampoline park has an admission fee, plus an hourly charge. The graph displays the total cost from 3, 4, 5, and 6 hours of play. Determine the hourly charge, assuming the relationship is linear.
Rate of change = $ ____________ per hour
Answer: ✔4.50
Trampoline Park has an admission fee, plus an hourly fee of $4.50. Determine the admission fee that the trampoline park charges.

What is the initial value?
Answer: ✔ 5.00
A group of students is collecting books to add to their library. The table shows the number of books in the library after 1, 3, and 5 days. If the relationship between days and books continues to be linear, which ordered pairs could appear in the table? Check all that apply.
Answer: ( 2, 23)
Answer: ( 7, 48)
Emily and John each ran at a constant speed for a 100-meter race. Each runner's distance for the same section of the race is displayed below. Who had a head start, and how big was the head start?
Answer: John and 10
Emily and John each ran at a constant speed for a 100-meter race. Emily gave John a 10-meter head start. Use the given data below to determine who won the race and by how many seconds.
__________ won the race by about_________ seconds
Answer: Emily and 2 seconds
Taleen has 8 stamps in her collection, and she decides that each month she will add 3 stamps to her collection.
What does the rate of change represent?
Answer:✔ number of stamps added monthly
What is the rate of change?
Answer: ✔3

What does the initial value represent?
Answer: ✔starting number of stamps
What is the initial value?
Answer: ✔8
Razi is filling bags with party favors for his birthday party. The table to the right shows the number of bags he still needs to fill after 4, 5, 6, and 7 minutes. If he is working at a constant rate, what was the initial number of party favor bags Razi had to fill?
Answer: ✔5
Seung and Razi are both filling party favor bags for their birthdays at a constant rate. Razi's progress is shown in the table.
After 3 minutes Seung had 34 bags remaining to be filled, and after 4 minutes he had 31 bags remaining.
Compare Seung and Razi's bag-filling progress.
Each minute Seung fills ____________ than Razi.
Answer:✔one less bag
The graph shows the charges of an instructor. The instructor charges an initial fee and then an hourly rate for private lessons. Determine the instructor's hourly charge from the graph.

What is the hourly charge?
Answer: ✔$8.00
The graph shows the charges of an instructor. The instructor charges an initial fee and then an hourly rate of $8.00 an hour for private lessons. Determine the instructor's initial charge from the graph.
Answer: ✔20.00
Mr. Lopez, a Language Arts teacher, has his students read a certain number of pages out loud in class to start a book, and then a set number of pages for homework each night to complete the book. The graph displays the total number of pages read each day.

What does the point (0, 35) represent?
Answer: ✔ The students read 35 pages in class to start the book.
A water park charges a rental fee plus an hourly fee for inflatable inner tubes. The total costs of 3, 4, and 5 hours are $8.00, $8.75, and $9.50, respectively.

Make a table or draw a graph to determine the rental fee and the hourly fee the water park charges.

What is the cost of the hourly fee?
Answer: ✔ $0.75
What is the cost of the rental fee?
Answer: $5.75
Given the graph of a linear function, identify the steps used to find the initial value. Check all that apply.
Answer: ✔ Find the rate of change using rise over run.

Answer: ✔Find corresponding y values when x = 2, x = 1, and x = 0. Then plot the points to finish the line.

Answer: ✔ The initial value corresponds to the y value when x = 0.
A table contains the ordered pairs (3, 42.25) and (5, 50.75). If the relationship in the table is linear, explain how to find the initial value.
Answer: ✔ First you can find the rate of change to be 4.25. Then you can subtract 4.25 repeatedly until you get to an output with an input of zero. The initial value is the output when the input is zero. The initial value after subtracting 4.25 three times is 29.50.
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