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 10 Interactive Maths - Second Edition


Models of physical situations are often arrived at by recording the values of variables in a table and by sketching graphs. Examining the tabulated values and the graph, we try to define the relationship between the variables by an equation. The equation thus derived is called a mathematical model.

If the value of a dependent quantity changes as a result of changes in the value of an independent quantity, then we say that one quantity varies with respect to the other. However, the type of variation depends on the relationship.

Direct Proportion (or Variation)

A cyclist's progress over a journey of 120 km is recorded. The results are tabulated below and plotted on a graph.

In such a case, we say that:

This is written as:

From the tabulated values, we find that:

In general:

The constant k is called the constant of variation or the constant of proportionality.

Graphically, this relation takes the shape of a straight line with gradient equal to the value of k.

Example 9

If y varies directly as x and y = 15 when x = 5, find the formula connecting x and y. Hence find y when x = 8.


This is the required formula.

Example 10

Use the following diagram to find the relationship that exists between x and y.  Hence find y when x is 9.5.


Key Terms

mathematical model, variation, direct proportion, direct variation, constant of proportionality, constant of variation

| 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 | Tutor Software | Maths Software Platform | Trial Maths Software |
| Feedback | About mathsteacher.com.au | Terms and Conditions | Our Policies | Links | Contact |

Copyright 2000-2020 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.