Activity 1. - The y intercept: Understanding the Concept.

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 coefficient of x represented by “m” to 2. Then change the constant term represented by “b” in the equation, and note the exact differences in the graph. As you do so, try to discover a relationship between the constant term and the 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.

y = 2x

y = 2x + 4

y = 2x – 5

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

Answer these questions:

(a) What relationship do you notice between the y-intercept and the graph? Explain.

(b) Based on your discovery, explain what you understand the y-intercept to be.

(c) (i) What is the value of “b” in the equation, y = x ?

(ii) Say what is unique about the graph of y = x and explain why.

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