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 ?