Exploring the properties of linear functions SC
Students should be able to identify the gradient and intercept of linear functions. They should be able to find the equation of the line through two given points, or through one point with a given gradient and interpret the gradient of a straight line graph as a rate of change.
When plotting linear graphs some pupils may draw a line segment that stops at the two most extreme points plotted
Some possible misconceptions include not rearranging the equation of a straight line given in an alternative form. For example, they may suggest that the line y – 4x = 12 has a gradient of -4. Some students may think that gradient = (change in x) / (change in y)’ If they understanding of gradient is not secure students may think that the horizontal section of a distance time graph means an object is travelling at constant speed or that a section of a distance time graph with negative gradient means an object is travelling backwards or downhill.
Links and Resources
This Mathcentre resource covers aspects of functions and graphs. It includes a unit “Linear Functions” which is about linear functions and their graphs. It starts by introducing functions and linear functions. It then goes on to describe dependent and independent variables. It then goes into more detail on functions and linear functions. It then describes how to plot the graph of a linear function using coordinate pairs. It then has an example question. They could be used to review, and consolidate students’ knowledge and understanding of linear functions. Students could be given this to read for homework and then asked to design their own question based on what they have read. This could be shared at the start of the next lesson.
This video resource from Teachers TV demonstrates a practical applications of mathematics using straight line graphs to compare the price difference of two mobile phone deals.
Formulae are developed and graphs drawn to show how the cost of 'pay as you go' and 'monthly contract' tariffs compare. Students are then challenged to determine how many days a month someone using pay as you go can access the internet without exceeding the annual cost of a monthly contract. It also reminds
Calculations are performed in stages throughout the video, offering a pause point for teachers to hold a freeze frame on screen while students discuss the problem and perform the calculations themselves. This could be used at the start of a series of lessons where you are likely to be using straight line graphs. You can use it to discuss the gradient and intercept of a straight line. Ask question such as what happens when the gradient gets bigger / smaller / negative?