Linear functions This graph is the straight line y = 3x. [ A4.2 Core Starter] This graph is the straight line y = 3x. Investigate the connection, if any, between this graph and the graph of x = 3y. In other words, what happens when the x and the y are swapped over? Choose some other straight line graphs to investigate and compare: For example: y = x + 2 and x = y + 2 Preamble A short investigation practising plotting points in all four quadrants. The discussion of pupils’ strategies on completing is important. Possible content Generating and plotting straight line graphs Resources Squared paper for grids (at this stage pupils would benefit from drawing the straight lines, rather than using some form of graph plotter). Ideally grids should be pre-drawn to maximise thinking, and minimise time wasting drawing and labelling axes. Solution/Notes Pupils own observations including: Lines make equal angles to increasing x- and y- axes respectively. Lines intersect at (p, p) where p is a linear function of c in y = mx + c (and also of m if c is kept constant.). Original Material © Cambridge University Press 2010 Original Material © Cambridge University Press 2010