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

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

Do This:

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

Here are some examples. Below each equation note thedifference 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 thedifference 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) Whatsingle word would you use to describe what changed in each graph (BothClusters)?

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

(c) Writea brief comparison between the equations and graphs in the first cluster andthe second cluster.

(d) Writea general statement explaining the effect of the x coefficients on thegraphical models (include effect of positives and negatives)

TEACHER NOTES

This lesson incorporates the following teaching strategiesbases 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 technologyguidelines 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