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Equations of Lines: The Finale
We are at the finale of our module. In this subtopic, we will use all of the information we have learned to create equations of lines. We will discuss three forms of equations of lines in particular: standard form, slope-intercept form (or linear function), and point-slope form.
Important definitions include those for:
standard form
slope-intercept form
point-slope form
In this subtopic, we begin with a Relating Linear Equations and Their Graphs Activity, designed for use in the classroom and encourages students to become involved in the learning process. It is suggested that this exploration activity be completed before formally discussing equations of lines. At the conclusion of the activity, students should be proficient in recognizing the slope and y-intercept from an equation in slope-intercept form.
Relating Linear Equations and Their Graphs Activity
The objective of this cooperative learning activity is for the student to connect the concept of slope and the y-intercept from a linear equation to its graph. Since this activity is designed for exploration, it is best done before formally discussing forms of equations of lines.
The following activity is designed for two students working together; however, instructors may need or want to increase the number of students in one group.
The activity is conducted in two parts.
Part 1
Each pair of students is given a random equation (preferably in standard form) from the List of Equations. Note that these equations are grouped with the same slope, for instructor convenience. Depending on the number of students in your classroom, you may want to remove or add equations.
After each pair of students is given an equation, the instructor will need to give each student a Relating Linear Equations and Their Graphs Worksheet along with a copy of Graph Paper. Students are then asked to find the following information about their line:
Find four points on your line.
Find the slope of your line.
From this information, pairs of students will then look for other pairs of students that have the same slope as their own line. In a newly formed (larger) group, students complete the following:
Graph all line on one coordinate system.
What conclusion can be made from the graph?
Solve your equation for y and compare your equation with other pairs of students in your group.
What conclusions can be made?
Part 2
Now, in part 2, the original pairs of students get back together with their original equation and find the y-intercept of the line.
After each pair of students has found the y-intercept of their original line, they should find other pairs of students in the classroom with the same y-intercept. In the newly formed group, the students complete the following:
Graph all lines on one coordinate system.
Compare your equations from step 6 in part 1 with other pairs of students in the intercept group. What conclusions can be made?
At the end of the activity, instructors may wish to bring the class together and discuss the conclusions that were made from Part 1 and Part 2.
Instructors may assess this activity by the level of student participation during the activity and responses on the Relating Linear Equations and Their Graphs worksheet.
Note that this activity is a modification of "Cooperative Learning Activities" by Sue Parsons (Cerritos College) presented at the NISOD International Conference on Teaching and Leadership Excellence on May 21-24, 1995 in Austin, Texas.
Activity two, Lecture Notes Class Activity, is for use by the instructor with students or as an individual student activity. In the lecture notes, we define important terms and create equations of lines when given the slope and y-intercept or two points on a line. Elements within the lecture notes may be used to assess understanding of the content.
Activity three, Phone Bill Project, can be used as an in-class group activity or take-home assignment. At the conclusion of the activity, students should be able to recognize the importance of linear equations in a real life-application. Extensions of this activity can be done to include a Water Bill Activity consisting of piecewise-defined functions.
In the summary, instructors are provided with a Pre-Test and Post-Test of the subtopic. Instructors may choose to use both tests, or only the Post-Test as a final assessment.