Linear equations and cell phone plans
This lesson has been prepared for 9th grade Algebra (Algebra 1A). The goals of
the lesson are for students to plot data points on a graph, calculate the equation for the
line graphed and finally to determine the y-intercept and slope of the line. Overall students
will gain conceptual knowledge of a linear equation and will be exposed to a real life
application of linear equations.
Pass out the problem to the students. Have the students read the problem
silently, then choose a student to read the problem out loud. First ask the students to
state the goal of the activity. The students need to understand what they are attempting
to find. Ultimately, students want to find the base rate a cell phone customer is charged
every month and how much the customer is charged per minute.
Questions to initiate discussion:
1. How many minutes did you talk July? How much did that cost?
2. How many minutes did you talk August? How much did that cost?
3. How many minutes did you talk September? How much did that cost?
4. Can you organize this data into a table?
Students will recognize that they have been making tables of (x,y) coordinates to graph on
the coordinate plane. Some students will make the connection and graph the data points.
The students should know how to calculate the slope of this line in order to find the
equation of the line in the form y=mx+b.
5. What does the slope represent?
6. What does it mean when the line crosses the y-axis?
The students can find the solution by making a table of data points and then graphing the
points on the xy-coordinate plane. The equation of the line can then be calculated.
How much are you really being charged per
minute to talk on your cell phone?
You receive your phone bill for July, August and
September, which comes to a grand total of $260.50.
Shocked with the outrageous price, you need to find out
how much you are being charged per minute. So you call
the customer service line and the information you receive
still does not tell you how much each minute costs.
The representative does tell you that in July you talked
for 180 minutes at a total cost of $88.00. In August you
used 50 minutes at a total cost of $42.50. And finally in
September you talked on your cell phone for 300 minutes
and you were charged $130.00.
How much are you charged per minute?
And what is the base rate to use your phone per month?
Solution
Table of data points
Minutes (x)
180
50
300
Cost (y)
$88
$42.50
$130
Equation of the line calculated from the data points:
Y = .35x + 25
How much are you charged per minute? $.35
What is the base rate to use your phone per month? $25