Defining lines by points, slopes and equations

This resource develops the concept of finding the slope and equation of a linear graph defined by pairs of coordinates. There is also work on using the slope and y-axis intercept of a straight line to derive its equation.

The initial task for students to consider is to use proportional reasoning to calculate a change in x and a change in y for a straight line graph. The next task considers three points and determining if they lie on a straight line. The concepts are linked to a sequence of right-angled triangles. There is then a matching exercise where cards are collected with worded statements, graphical representations, and points that a line passes through.  

There are pre-lesson and post-lesson formative assessment tasks. Detailed teacher notes give suggestions on questioning and how to use the resources. Full solutions are given for each of the sections.

This is a concept development lesson from the Mathematics Assessment Resource Service, a collaboration between UC Berkeley and the Shell Centre team at the University of Nottingham. Further information on the collection is given here.