Topic: Parallel Lines and Properties of Slope

Level:

TI-81/82 Proficiency:

Menus/Keystrokes Needed:

Students should be familiar with how to define functions to be graphed using the Y= key and how to set up a standard viewing screen using Zoom 6.

Notes to Teachers:

The attached worksheet was given to the class to work on in groups of 3 after they had studied the concepts of rates of change, constant rates of change and slope-intercept form of equations of lines. These students had used the graphing calculators previously in class and had some rudimentary knowledge of how to use it. I walked around the room and served as a "technology consultant," but I left the groups to discuss and explore the mathematical questions posed on the worksheets themselves.

Students struggled the most with the "describe and compare" questions. For example, in the first section, almost every group wrote that the lines were parallel, but few went further than that until coaxed to look at other characteristics of the lines such as intercepts and in which quadrants the graph fell.

Overall though, my objectives for this lesson were met. Students worked cooperatively in groups, held meaningful mathematical discussion, and had some experience writing up their results. The use of the calculator enabled students to bypass the drudgery of hand constructing the graphs so they could get to the business of exploring slope. I collected worksheets from each groups and gave it a classwork grade and discussed the results in class the next day.

Extension:

Students who got through this lesson quickly were asked to explore how to find perpendicular lines. One group handed in the equations for the axes and another group discovered that y - x and y = -x were perpendicular. However, no one discovered the relationship of negative, reciprocal slopes to perpendicular lines. With more time, perhaps this might have happened.

Worksheet:

Name_________________________________ Date____________________
Algebra I Graphing Calculator Exploration 8.1-8.6 16 points

Section I

1. Describe and compare the graphs of y = 4x - 1 and y = 4x + 3.

2. Describe and compare the graphs of y = -2x - 2 and y = -2x - 5.

3. Write an equation whose graph is a line parallel to and
between the graphs of y = 2x + 3 and y = 2x + 4.7.

4. Write an equation whose graph is a line parallel to the graph
of y = -3x + 1 but with y-intercept (0,-5).

Section II

5. Describe and compare the graphs of y = 0.5x, y = 2x, y = 0.06x and y = 7x.

6. If m is positive, predict what will happen to the graph as m gets larger in the equation y = mx.

7. Write an equation of a straight line in quadrants I and III steeper than y = 2x.

8. Write an equation of a straight line in quadrants II and IV flatter that y = -0.03x.

EXPLORE FURTHER:

Try to find 2 equations whose graphs are perpendicular lines. Use the ZOOM-SQUARE feature when testing your conjectures.

Theresa Choma, Glen Rock High School, Glen Rock, New Jersey 07452