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.

(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