Introduction
This unit plan is to be used in an Algebra I course. However, it could easily be incorporated into a Pre-Algebra course or into an Algebra II course as a review unit. The graphing calculator activities are designed to be completed with a TI-83 graphing calculator but could be modified for other types of graphing calculators. Before assigning the activities, some direction should be given on setting the calculator viewing screen and other options. Additional oral instructions may be necessary for some of the activities. The intention is for the bulk of each activity to be completed during the class period. Appropriate homework will also be assigned each day. Two quizzes should be given throughout the unit over the material covered up to that point, and questions related to the graphing calculator activities should be included. Similarly, the examination at the end of the unit should be composed of questions requiring the use of the graphing calculator and questions that do not require the use of the calculator.
Sequence of Lessons in the Unit
Day 1 – Slope of a Line
Objective: 1. Find the slope of a line, given the coordinates of two points on the line.
Introduce the concept of slope by taking the students to a staircase and having them explain how they move their feet to get upstairs. This process naturally leads into the definition of slope as rise over run. Demonstrate finding slope given the coordinates of two points on a line. Apply the concept of slope to real-world situations by discussing the grade of a road and the incline of a wheelchair ramp.
Day 2 – Slope of Linear Equations
Objective: 1. Determine the slope of a graph.
Have the students complete the Graphing Calculator Activity #1 in groups of two to discover the relationship between the slope and the equation of a line. After the students complete the worksheet, lead them in a discussion about their findings, emphasizing the effect of negative and positive slopes on the graph. Point out that all of the graphs on this worksheet pass through the origin if the students themselves do not mention this, and state that equations that do not pass through the origin will be investigated during the following class period. Also discuss the slopes and equations of vertical and horizontal lines.
Day 3 – Slope-Intercept Form of Linear Equations
Objectives: 1. Determine the x- and y-intercepts of a graph.
2. Write an equation in slope-intercept form given the slope and
y-intercept.
To introduce the concept of the y-intercept of a line, have the students
complete the Graphing Calculator Activity #2 in groups of two. Ideally,
this activity will lead the students to some of their own conclusions about
the equation 
. After the
students complete the activity, discuss the ideas that they have and lead
this into a discussion of determining the slope and y-intercept of a graph.
Also explore determining the x- and y-intercepts of a graph and writing
an equation in slope-intercept form given the slope and y-intercept. Apply
the concept of the slope and y-intercept to real-world situations by discussing
the charge of a long distance call given the charge for the first minute
and the charge for each additional minute. The y-intercept is represented
by the charge for the first minute and the slope is represented by the
charge for each additional minute.
Day 4 – Graphing Linear Equations
Objective: 1. Graph linear equations using the x- and y-intercepts or the slope and y-intercept.
Demonstrate how to graph linear equations using the x- and y-intercepts and using the slope and y-intercept. Discuss real-world situations that can be represented by linear equations such as charges for car rentals, catering, long distance telephone calls, and so forth. Graph a possible relationship between the number of hours slept the night before a test and the score received on the test in order to show students the relevance of the topic to their lives.
Day 5 – Writing Slope-Intercept Equations of Lines
Objectives: 1. Write a linear equation in slope-intercept form given the slope of a line and the coordinates of a point on the line.
2. Write a linear equation in slope-intercept form given the coordinates of two points on the line.
Day 6 – Point-Slope and Standard Forms of Linear Equations
Objectives: 1. Write a linear equation in standard form given the coordinates of a point on the line and the slope of the line.
2. Write a linear equation in standard from given the coordinates of two points on the line.
Day 7 – Parallel and Perpendicular Lines
Objective: 1. Write an equation of a line that passes through a given point and is parallel or perpendicular to the graph of a given equation.
Days 8 & 9 – Internet Project on Automobile Depreciation
The students should complete the Internet Project on Automobile Depreciation in pairs. The first class period should involve collecting the data from the Internet, and the second class period should involve doing the calculations on the graphing calculator and answering questions about the data and the equations. Before starting the activity, discuss scatter plots with the students. Emphasize the difference between a positive correlation, a negative correlation, and no correlation. Discuss the correlation coefficient (r) and how it is determined. The student worksheet should be self-explanatory.
Day 10 – Review of the Unit
Review the unit by giving the students graphs of linear equations and having them write the equations of the graphs in slope-intercept form and in standard form. The students can check their equations by graphing them on the calculator and determining if the graphs on the calculator match the original graphs.
Day 11 -- Examination
Graphing Calculator Activity #1
Directions: Graph the following equations on your calculator and make a sketch next to each equation. Choose two points on the line and use the slope formula to find the slope of each line.
1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
10. 
11. 
12. 
13. 
14. 
a. Write a comparison of the graphs of equations with a positive coefficient
of 
and a negative coefficient
of 
.
b. Write a description of how the coefficient of 
affects the graph of the equation.
c. Without graphing, predict what the graph of 
will look like.
d. Write an equation of a line whose graph has a left-to-right downward slope.
e. Write an equation of a line whose graph lies between the graphs of 
and 
.
Graphing Calculator Activity #2
Exploring 
Directions: Graph the linear equations and answer the questions about each group of equations.
1. Graph the equations: 
, 
, 
, 
b. What is different about these graphs?
, 
, 
, 
b. What is different about these graphs?
, 
, 
, 
b. What is different about these graphs?
, 
, 
, 
b. What is different about these graphs?
6. In general, what conclusions can you make about the constant term?
Graphing Calculator Activity #3
Writing Equations of Lines
1. Record your height in inches and shoe size on the chart in the classroom. Female students should record their corresponding men’s shoe size if they know it or subtract 1.5 from their women’s size. Make a table to record the data for the entire class, using the height as the independent variable and the shoe size as the dependent variable.
2. In pairs, make a table of the data on your TI-83, and plot the graph. Sketch the scatter plot on a piece of graph paper, including a sketch of what appears to be the best-fit line.
3. Choose two points on your line whose coordinates are whole numbers. The points do not have to be actual data points. Record the coordinates below:
Difference between actual and predicted:
for the data. Record the values for a and b below:
b =
8. Would it be reasonable to sell shoes by a person’s height? Why or why not?
Graphing Calculator Activity #4
Writing Equations of Lines
Directions: Write an equation of a line described by each of the following statements. Write the equations in both slope-intercept form and standard form. Graph the slope-intercept form of the equations to check whether it fits the description.
1. A line with positive slope and y-intercept 4
2. A line with negative slope that passes through the origin
3. A line with positive slope that passes through (4, -3)
4. A line with negative slope that passes through (-5, 2)
5. A line with slope 0 that passes through (1, -1)
6. A line with positive slope and x-intercept –2
7. A line with negative slope and y-intercept 4
8. A line with no slope that passes through (-2, 5)
9. A line with negative slope and x-intercept –6
10. A line with no slope and y-intercept –7
Graphing Calculator Activity #5
Directions: Graph the linear equations and answer the questions
about each group of equations.
1. Graph the equations: 
, 
, 
, 
a) What is the slope of each of these lines?
b) Describe the similarities and differences among the graphs.
2. Graph the equations: 
, 
, 
, 
a) What is the slope of each of these lines?
b) Describe the similarities and differences among the graphs.
3. Based upon the previous two examples, what conclusions can you make?
4. Graph the equations (use ZoomSquare): 
and 
a) What is the slope of each of these lines?
b) Describe the similarities and differences among the graphs.
5. Graph the equations (use ZoomSquare): 
and 
a) What is the slope of each of these lines?
b) Describe the similarities and differences among the graphs.
6. Graph the equations (use ZoomSquare): 
and 
a) What is the slope of each of these lines?
b) Describe the similarities and differences among the graphs.
7. Based upon the previous three examples, what conclusions can you make?
Automobile Depreciation Internet Project
Although depreciation for automobiles is not always linear throughout the entire life of the automobile, some models depreciate somewhat linearly the first ten years. In this project, you and your partner will choose five models of automobiles to investigate for the years 1987 - 1997. Use the following Internet site to find the current market prices for the automobiles:
Edmund’s Automobile Buyer’s Guide http://www.edmunds.com/edweb/
Choose the link "Used Car and Truck Prices & Reviews."
1. Record your data in the tables provided on the page entitled Data for Automobile Depreciation. Note that you should record the age of the automobile (not the year) and the current market price.
2. Plot each set of data on a coordinate plane on a piece of graph paper.
Clearly label the axes and provide a title for each graph. Draw what appears
to be the best-fit line and write an equation in slope-intercept form.
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3. For each automobile, make a table of the data on your TI-83 and plot
the graph. Under the STAT menu, calculate the linear regression 
for the data. Record the values for the slope, y-intercept, and correlation
coefficient below:
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How closely do your best-fit line equations match the linear regressions
provided by the TI-83?
4. Based upon your calculations, answer the following questions:
Data for Automobile Depreciation
Automobile:
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Automobile:
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Automobile:
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