Mathematics / Year 9 / Number and Algebra / Linear and non-linear relationships

View on Australian Curriculum website Australian Curriculum, Assessment and Reporting Authority
Curriculum content descriptions

Find the midpoint and gradient of a line segment (interval) on the Cartesian plane using a range of strategies, including graphing software (ACMNA294)

  • investigating graphical and algebraic techniques for finding midpoint and gradient
  • recognising that the gradient of a line is the same as the gradient of any line segment on that line
General capabilities
  • Numeracy Numeracy
  • ICT capability Information and Communication Technology (ICT) capability
ScOT terms

Cartesian coordinates,  Gradients,  Midpoints

Interactive resource

EagleCat: linear graph

Explore the graphs of linear equations in the form y = mx + c. Observe changes to the gradient and y-intercept under various transformations. Alternately, change the equation and observe changes in the y-intercept or change the y-intercept and see how the equation changes.


BBC Bitesize: graphs - revision

These illustrated information sheets revise the rules for vertical and horizontal lines and the meaning of m and c in the rule y = mx + c. Students find the rule for a given linear graph. Tables of values are created so that graphs can be plotted. This resource is one of a series of online resources from the BBC's Bitesize ...


Introduction to slope

In this animated presentation students are introduced to the mathematical concept of slope (or gradient) of a straight line. The mathematical definition of slope is explained in terms of, and derived from, two practical contexts.

Teacher resource

reSolve: Gradient and Tangent

This sequence of two lessons investigates gradient and angle by applying the tangent ratio to find the angles represented by a road sign or the angle of a street. In the first lesson, students research what a road grade is and determine the actual angle of a road given its grade. They then construct their own road sign ...

Teacher resource

Secondary mathematics: different representations

These seven learning activities, which focus on 'representations' using a variety of tools (software) and devices (hardware), illustrate the ways in which content, pedagogy and technology can be successfully and effectively integrated in order to promote learning. In the activities, teachers use different representations ...

Interactive Resource

Laptop wrap – a slippery slope

Distance, midpoint and gradient are investigated as students design an Excel spreadsheet and make a Smart Notebook presentation on ski-lifts. Students then contribute to a discussion on the steepest street in the world. 

Interactive Resource

Laptop wrap: Parallelendicular

Students construct a series of GeoGebra applets that investigate the parameters gradient and intercepts of straight lines. They reinforce this knowledge with Microsoft Math 3.0. 

Interactive Resource

The Cartesian plane

This is a four-page HTML resource about solving problems involving the Cartesian plane. It contains three videos and four questions for students to complete. The resource discusses and explains the use of coordinates and finding the distance between two points.

Teacher resource

reSolve: Real World Algebra: Linear Functions

This sequence of two lessons explores real world, algebraic, numeric and graphical representations of linear functions, focussing on the gradient of linear functions. Students use images of everyday objects and inscribe straight lines, then use Geogebra to explore the algebraic representation of their lines. Each lesson ...

Teacher resource

TIMES Module 29: Number and Algebra: introduction to coordinate geometry - teacher guide

This is a 22-page guide for teachers. This module introduces coordinate geometry. The introduction includes finding the distance between two points, finding the coordinates of the midpoint between two points, determining the gradient of a line and determining the equation of a line.

Teacher resource

TIMES Module 35: Number and Algebra: proportion - teacher guide

This is a 22-page guide for teachers. The module introduces the idea of direct proportion and illustrates its many uses in science, commerce and measurement. It looks at ratios, gradients and fractions. A history of the development and use of proportion concludes the module.

Teacher resource

Coordinate geometry

This is a website designed for both teachers and students that addresses coordinate geometry from the Australian Curriculum for year 9 students. It contains material that shows the connection between algebra and geometry through graphs of lines and curves. There are pages for both teachers and students. The student pages ...