## Lesson Plans from the ADAPT Program

#### Date of this Version

1988

#### Abstract

Using *x as the independent variable*, draw one graph plotting: x vs A, x vs B, and x vs C. For each plot, connect the corresponding points with a smooth, best fit line or curve. (One graph of a data set by each person in your group is sufficient for now.)

The mental power of a linear relationship is our ability to use it to predict behaviors that we have not measured! So far we have used Cartesian (named for French mathematician René Descartes) graphs (see lab #3). Most of our labs have consisted of taking data, plotting the data on a Cartesian graph, and then finding the mathematical relationship between the variables by finding the slope and the starting value from the graph. However, not all graphs produce straight lines! The curves at the right are drawn from relationships between y and x called power laws. The general equation would look like y = Ax^{m} where A and m have numerical values. On Cartesian graph paper we can only make guesses at A and m. To find them we need to use log-log graph paper!