G S Rehill's Interactive Maths Software Series - "Building a Strong Foundation in Mathematics" from mathsteacher.com.au.

Order a 12-month Year 7 Interactive Maths software Homework Licence for only $19.95. Order a 12-month Year 8 Interactive Maths software Homework Licence for only $19.95. Order a 12-month Year 9 Interactive Maths software Homework Licence for only $19.95. Order a 12-month Year 10 Interactive Maths software Homework Licence for only $19.95.

Year 7 Interactive Maths - Second Edition


Modelling Linear Relationships

Tables and graphs are useful to find a pattern between the y-coordinate and the x-coordinate.


Using Tables

We can find a pattern in coordinates by listing their ordered pairs in a table.


Example 7

Consider the following table.

Table of ordered pairs

a.  Describe the relationship between the y-coordinate and the x-coordinate in words.
b.  Find the algebraic relationship between x and y.

Solution:

a.  By trial and error, we look for a relationship between the values of x and y.

     We can describe the relationship between x and y in words as follows:
     The y-coordinate is twice the x-coordinate
     This means y is twice x.

b.  So, the algebraic relationship between the x-coordinate and y-coordinate is:

y = 2x


Using Graphs

We can find a pattern in coordinates by drawing a graph of their ordered pairs.


Example 8

a.  Plot the following points on a Cartesian plane:
     A(1, 3), B(2, 6), C(3, 9), D(4, 12), E(5, 15), F(6, 18)
     Use a ruler to join the points A, B, C, D, E and F.

b.  Describe the relationship between the y-coordinate and the x-coordinate in words.
c.  Find the algebraic relationship between x and y.

Solution:

Linear relationship on a Cartesian plane

b.  We notice that the points lie on a line.  Such a pattern is called a linear relationship because it represents a straight line relationship between the coordinates of the points.

We can describe the relationship between x and y in words as follows:  The y-coordinate is three times the x-coordinate.  This means y is three times x.

c.  So, the algebraic relationship between the x-coordinate and y-coordinate is:

y = 3x


Example 9

a.  Plot the following points on a Cartesian plane:
     A(2, 0), B(3, 1), C(4, 2), D(5, 3), E(6, 4) and F(7, 5)
     Use a ruler to join the points A, B, C, D, E and F.

b.  Describe the relationship between the y-coordinate and the x-coordinate in words.
c.  Find the algebraic relationship between x and y.

Solution:


Linear relationship on a Cartesian plane

b.  We notice that the points lie on a line.  Such a pattern is called a linear relationship because it represents a straight line relationship between the coordinates of the points in the pattern.

We can describe the relationship between x and y in words as follows:
The y-coordinate is two less than the x-coordinate

c.  So algebraically, the relationship between the x-coordinate and y-coordinate is:

y = x - 2


Using a Difference Pattern

When we look for a pattern in ordered pairs, we can find the difference between two successive values of y.  This allows us to find a rule as illustrated below.

Consider the following table.

Analysis of the table of x and y coordinates reveals the pattern difference in the y values is 2

We notice that the values of x increase by just one at a time and the difference between the successive values of y is 2.  So, the rule starts off with y = 2x.  Will this give a correct answer from the table?  Let us check.

When x =1, y = 2

The answer is no.  From the table, when x = 1 the value of y should be 5.  How do we change our answer from 2 to 5?  We should add 3.

The rule becomes y = 2x + 3

Check the rule to see if it is correct:


Key Terms

tables, graphs, linear relationships, difference pattern


| Home Page | Order Maths Software | About the Series | Maths Software Tutorials |
| Year 7 Maths Software | Year 8 Maths Software | Year 9 Maths Software | Year 10 Maths Software |
| Homework Software | Laptop Schools | Tutor Software | Maths Software Platform | Trial Maths Software |
| Feedback | About mathsteacher.com.au | Terms and Conditions | Our Policies | Links | Contact |

Copyright 2000-2014 mathsteacher.com Pty Ltd.  All rights reserved.
Australian Business Number 53 056 217 611

Copyright instructions for educational institutions

Please read the Terms and Conditions of Use of this Website and our Privacy and Other Policies.
If you experience difficulties when using this Website, tell us through the feedback form or by phoning the contact telephone number.