Superlesson
Project 2-1
Advanced Algebra
Chapter 2, Linear Functions, Equations, and Inequalities
Cable television has been a booming business in the United States for more than a decade. As the number of cable customers has grown, so have companies' rates and expenditures. Explore some trends in the cable television business using linear functions and equations.
Part A, Direct Variation and Linear Functions
1a. Graph the cable companies' monthly pay rate for the years 1982 to 1997.
b. Is the relationship you see in a approximately linear?
2a. Graph the cable companies' programming expenditures for the years 1986 to 1993.
b. Is relationship you see in 1a approximately linear?
3a. Pick two points from 2a and assume they define a linear function that describes cable companies' expenditures. Find the slope of the line between those two points.
b. Pick two other points from 2a and find the slope of the line between those two points.
c. Are your answers to 3a and 3b close? Explain what this means.
Part B, Solving Equations
4. Use the graph you made in question 2 to predict what cable companies' expenditures will be in the year 2000.
5. Suppose the equation to model the cable companies' expenditures could be written as: y = 281 x - 556,033. Solve this equation to calculate the expenditures in the year 2000.
6. How close are your answers to questions 4 and 5?
Part C, Analyzing Equations of Lines
7. Cable companies' basic revenue from subscriber services for the years 1986 to 1995 is a fairly linear function.
a. Graph this line.
b. Pick two data points and use them to calculate the slope of the line that describes these data.
8a. Use the slope you just calculated and the point (1986, 4891) to write the equation of the line in point-slope form.
b. Rewrite your answer to 8a in slope-intercept form.
Part D, Making Connections
9. Sunflower Cablevision is a cable provider in Kansas. Read about their set up and monthly rates.
a. How much does basic service cost each month?
b. How much does basic cable installation cost?
c. Write an equation that relates t, the total cost of service, and n, the number of months of service.
d. Use your equation in 9c to calculate how many months a family can get cable for $300.