how do you know the initial value of a linear relation?
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How do you know the initial value of a linear relation?. A 1400 gallon pool is emptied at a rate of 350 gallons per hour. In this lesson you will learn how to determine the initial value of a linear function by interpreting all four representations of a function. - PowerPoint PPT PresentationTRANSCRIPT
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How do you know the initial value of a linear relation?
A 1400 gallon pool is emptied at a rate of 350 gallons per hour.
![Page 2: How do you know the initial value of a linear relation?](https://reader036.vdocument.in/reader036/viewer/2022062517/5681332e550346895d9a2c7e/html5/thumbnails/2.jpg)
In this lesson you will learn how to determine the initial value of a linear function by
interpreting all four representations of a function.
![Page 3: How do you know the initial value of a linear relation?](https://reader036.vdocument.in/reader036/viewer/2022062517/5681332e550346895d9a2c7e/html5/thumbnails/3.jpg)
Let’s ReviewLet’s Review
An ice cream cup is $2.00 plus $0.50 for each additional topping.
x (toppings)
y (cost)
0 $2.00
1 $2.50
2 $3.00
3 $3.50
Initial value = $2.00
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Let’s ReviewA Common Mistake
An ice cream cup is $2.00 plus $0.50 for each additional topping.
Initial value = 0.50Incorrect!Initial value = 2.00
It happens 1 time, with 0 toppings!
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Let’s ReviewCore Lesson
A 1400 gallon pool is being emptied at a rate of 350 gallons per hour.
Initial value = 1400
Let W be the gallons remaining after T hours.
W = -350T + 1400
Initial value = 1400
Constant
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Let’s ReviewCore Lesson
T (hours)
W (remaining
gallons)
0 1400
1 1050
2 700
3 350
1400Initial value =
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Let’s ReviewCore Lesson
100100
Initial value = 1400
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Let’s ReviewCore Lesson
William purchased a $60 bicycle and he will earn $6 per hour delivering newspapers.
Initial value = -60
y = 6x – 60
Initial value = -60Initial value =
x (hours)
y (total amount)
0 -60
1 -54
2 -48
3 -42
Initial value = -60-60
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In this lesson you have learned how to determine the initial value of a linear function by
interpreting all four representations of a function
![Page 10: How do you know the initial value of a linear relation?](https://reader036.vdocument.in/reader036/viewer/2022062517/5681332e550346895d9a2c7e/html5/thumbnails/10.jpg)
Let’s ReviewGuided Practice
Jennifer made 100 necklaces and gave away 3 per week.
Identify the initial value in each representation.y = -3 – 1.75x
x y
-4 -5
-1 2.5
2 10
4 15
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Let’s ReviewExtension Activities
A glider takes 90 minutes to land. The position (P), in feet, at any given time (t) can be found using the equation: P = -5(t – 90)
What was the initial height (value) of the glider at takeoff?
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Let’s ReviewExtension Activities
Running back Joseph Addai signed a contract with the New England Patriots worth $725,000 per year plus a $75,000 signing bonus. What is the initial value of that contract?Explain.
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Let’s ReviewQuick Quiz
Given the table of values, which choice shows the correct initial value?
x y
-3 -6
-1 -8
3 -12
6 -15
a) -6
d) -10
c) -9
b) -8
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Let’s ReviewQuick Quiz
The high school senior class planned a graduation reception for parents and friends at a local restaurant. They held fund-raisers during their 12th grade year to raise the money. The restaurant charges $150 for the room and $10 per person for food and drinks. What is the initial value?