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How do you construct a function to model a scenario?. A wild animal park opens with 100 antelope and the population grows 5 antelope per year. In this lesson you will learn how to construct a linear function by calculating the slope and y-intercept given any representation. - PowerPoint PPT Presentation
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How do you construct a function to model a scenario?
A wild animal park opens with 100 antelope and the population grows 5
antelope per year.
In this lesson you will learn how to construct a linear function by
calculating the slope and y-intercept given any
representation.
Let’s ReviewLet’s Review
A linear function has a constant rate of change (slope) and an
initial value (y-intercept).
Every x is tripled, then increased by 2.y = 3x + 2
x y
0 2
1 5
2 8
3 11
5 - 21 - 0 31
Let’s ReviewA Common Mistake
The cost (C) for a cell phone plan is $30 for a month for unlimited minutes.
Incorrect, this would indicate an infinite
cost for 30 minutes of use (slope is not
defined).
Correct, cost is $30 for any amount of
minutes (slope is 0).
Let’s ReviewCore Lesson
A wild animal park opens with 100 antelope and the population grows
by 5 antelope every year.
Y-intercept Slope
y = 100 + 5x
Let’s ReviewCore Lesson
x (years) y (antelope)
0 100
1 105
2 110
3 115Y-intercept
51 105 - 1001 – 0
y = + x100Slope =5
15 5
Let’s ReviewCore Lesson
Slope =
Y-intercept
y = + x100 5
102
10
25
In this lesson you have learned how to construct a linear
function by calculating the slope and y-intercept given any
representation.
Let’s ReviewGuided Practice
Construct a linear function using the graph provided below.
Let’s ReviewExtension Activities
Construct a linear function for each of the given representations.
x y
0 -11
5 -41
15 -101
30 -191
Multiply x by 0.6 and add 7
Let’s ReviewExtension Activities
Write a linear function for this scenario. Make a table or a graph to help before you write it.
Parking Costs
up to 1 hour . . . . $3
each additionalhour . . . $1.50
Let’s ReviewQuick Quiz
Jordan’s movie rental company charges a monthly fee of $5.00 plus an additional cost of $1.25 per movie rental. Which of these equations represents the total monthly cost (c) of renting (x) movies?
a) C = 1.25x + 5.00 b) C = 3.75x + 5.00 c) C = 5.00x + 1.25 d) C = 5.00x + 3.75
Let’s ReviewQuick Quiz
Which is the graph of y = -3x + 5 ?