Games that Teach: Algebra v. Cockroaches

THE EQUATION OF A LINE

If you ask most people who have been through high school mathematics what the equation of a line is, a surprising number can spit out "Y equals m x plus b", or y = mx + b. Many of them can even tell you that the "m" stands for the SLOPE, and the "b" stands for the Y-INTERCEPT, and that the number that we pick for each of these parameters controls the appearance of the graph of the line that we get.

But I also don't think many people understand why this equation is so important. Part of the answer is that this particular equation ISN'T that important. Though there are many examples of processes that behave like a line, most often we need much more complicated equations or functions to describe real world phenomena. But what IS important about the equation of the line are the techniques we will use to analyze equations of polynomials of which "mx + b" is an example. In fact, analyzing y = mx + b is one of the simplest cases of a function that we can analyze, which is why it is discussed so often.

To understand how to analyze our equation of a line, and how changing the values of m and b affect the shape of our line, I have been using the game below called Algebra v. Cockroaches, where students need to fill in the equation of the line that the cockroaches are traveling on to be able to exterminate them.

y = mx + b