Modelling Linear Relationships 1. Ralph's Rental Company has many tools that are available for rent. For the rental of their post-hole digger, the company charges a $20 fixed price, plus $5 per hour. This can be represented by the equation C = 5n + 20 where C represents the total rental cost, and n represents the number of hours rented. The goal of this section is to help you develop equations on your own. We will look at tables of values, first differences, and graphs. a) Complete the table of values showing the rental costs for 8 hours. The chart has been started for you. Number of Hours Cost in Dollars First Differences 25-20=5 Rented 20 25 1 2 4 8 * sub in n = 0 to find 'C' C = 5n + 20 C= 5(0) + 20 C = 0 + 20 C = 20 Example : b) Complete the first differences for the above situation. Note: As the number of hours rented (n) increases by 1, the cost (C) increases by 5. Therefore, the relationship is linear, with a slope of 5. The slope is the same as the first differences (since the independent variable 'n' increases by 1 in the table). In general, we can make a few notes about our equation and how it relates to the description given in the example. C = 5 n + 20, Hourly Rate (Slope/Rate of Change) Fixed Cost (C-Intercept)

Modelling Linear Relationships 1. Ralph's Rental Company has many tools that are available for rent. For the rental of their post-hole digger, the company charges a $20 fixed price, plus $5 per hour. This can be represented by the equation C = 5n + 20 where C represents the total rental cost, and n represents the number of hours rented. The goal of this section is to help you develop equations on your own. We will look at tables of values, first differences, and graphs. a) Complete the table of values showing the rental costs for 8 hours. The chart has been started for you. Number of Hours Cost in Dollars First Differences 25-20=5 Rented 20 25 1 2 4 8 * sub in n = 0 to find 'C' C = 5n + 20 C= 5(0) + 20 C = 0 + 20 C = 20 Example : b) Complete the first differences for the above situation. Note: As the number of hours rented (n) increases by 1, the cost (C) increases by 5. Therefore, the relationship is linear, with a slope of 5. The slope is the same as the first differences (since the independent variable 'n' increases by 1 in the table). In general, we can make a few notes about our equation and how it relates to the description given in the example. C = 5 n + 20, Hourly Rate (Slope/Rate of Change) Fixed Cost (C-Intercept)

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

Modelling Linear Relationships
1. Ralph's Rental Company has many tools that are available for rent. For the rental
of their post-hole digger, the company charges a $20 fixed price, plus $5 per hour.
This can be represented by the equation
C = 5n + 20
where C represents the total rental cost, and n represents the
number of hours rented.
The goal of this section is to help you develop equations on your own. We will look
at tables of values, first differences, and graphs.
a) Complete the table of values showing the rental costs for 8 hours. The chart
has been started for you.
Number of Hours
Rented
Cost in Dollars
First
Differences
25-20=5
20
1
2
3
4
25
6
7
8
* sub in n = 0 to find 'C'
C = 5n + 20
C = 5(0) + 20
C = 0 + 20
C = 20
Example :
b) Complete the first differences for the above situation.
Note: As the number of hours rented (n) increases by 1, the cost (C) increases by 5.
Therefore, the relationship is linear, with a slope of 5. The slope is the same as the
first differences (since the independent variable 'n' increases by 1 in the table).
In general, we can make a few notes about our equation and how it relates to the
description given in the example.
C = 5 n + 20,
Hourly Rate
(Slope/Rate of Change)
Fixed Cost
(C-Intercept)

Student Handout - Unit 3, Lesson 5
This information can also be represented by a graph:
Ralph's Rental
75
70
65
60
tun--3-
C= 5n + 20
55
50
45
rise # 15
40
slope = rise
35
30
run
25
20
= 15
C-intercept
of 20
%3D
5
-50
i9
10
Number of Hours
Summary
This type of equation can be developed from a written description by using the
general formula below.
C = (rate per item)n + (fixed amount)
or
Y = mx + b
Slope
Vertical intercept
Cost ($)

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