Activity 2. - The x coefficient or “m” in y = mx + b: Understanding its use.

Use the StraightLineEqn.xls tool, which displays a graph of an equation of the form:
y = mx + b.

Do This:

Using the tool, first change the value of the constant term represented by “b” to 0. Then change the x coefficient and note and discuss the changes in each graph. NOTE: To complete a change press the enter key after typing the new value.

Here are some examples. Below each equation note the difference in the graph.

CLUSTER #1:

y = 2x

y = 4x

y = 6x

You may try some of your own. When you get the connection, proceed.

Here are some more examples. Below each equation note the difference in the graph.

CLUSTER #2:

y = -2x

y = -4x

y = -6x

You may try some of your own. When you get the connection, proceed.

Answer these questions:

(a) What single word would you use to describe what changed in each graph (Both Clusters)?

(b) Considering the first cluster of graphs, explain the general relationship between the changes in the x coefficients and the corresponding graphs.

(c) Write a brief comparison between the equations and graphs in the first cluster and the second cluster.

(d) Write a general statement explaining the effect of the x coefficients on the graphical models (include effect of positives and negatives)

TEACHER NOTES

This lesson incorporates the following teaching strategies bases on the NCTM standards.

• Technology integration
• Interactive learning
• Concept-building through discovery
• Actively building new knowledge from experience and prior knowledge
• Discourse in mathematics
• Formulate explanations
• Mathematical literacy
• Using modeling to solve problems
• Making connections by investigating various models

In addition the lesson meets the following technology guidelines specified by Garofolo, Drier, Harper, Timmerman, and Shockey (2000):

• Applying technology to meaningful problems
• Employing technology to improve pedagogy
• Connect mathematical topics
• Use multiple representations