This lesson requires some pre-planning on the part of the teacher. You must take a list of equations (an example list is provided below) and graph these equations on photocopiable graph paper. This will give the students material to work with while learning the skill of determining equations from graphs.
Group Size: Whole class
1. Students will be able to derive the equation of a line from its graph.
Pre-made graphs that have been photocopied as handouts
This lesson requires some pre-planning by the teacher, as you must take graph paper and create several graphs of equations to hand out to the students. Record the equation for each graph on a key that you will use.
Begin the class by reviewing the cost curve information from the previous classes. Ask students to remind you the entire process of deriving a cost curve equation and graphing it. Focus particularly on the role that the slope and the y-intercept play in both the graph and the equation.
Next, review point-slope form and slope-intercept forms with the class. Ensure that the class is familiar with both forms and can accurately identify the encoded information within each form.
Now, inform the class that today they will be learning how to work "backwards", deriving equations from graphs rather than graphing pre-determined equations. Inform them of how this will ultimately be useful in determining equations from sets of data, which will in turn allow us to make mathematical predictions from statistically valid processes.
Hand out the worksheet you have created and have students follow along individually as you demonstrate how to find the equation from the first example. Make sure that the worksheet covers both examples of slope-intercept and point-slope form. Following is a list of suggested lines to graph:
y = 1/2x +3
y - 3 = -2 (x - 2)
y = -5/3x - 2
y + 2 = 1/3 (x - 5)
x = -4
y = 5