Videos: Linear Functions and Costs
What is a Linear Equation?
- You’re concerned about your cell phone bill for this month and you can’t remember how your plan actually works. You have been careful to keep track of how much data used each month and this month you have used 160 Mb. Using the payment information from your on-line banking you compile the following:
| Month | Mb of Data used | Amount paid |
| June | 120 | $40 |
| July | 80 | $30 |
| August | 200 | $60 |
- What is the independent variable and what is the dependent variable?
- Use a graph to determine the amount of your cell phone bill for this month.
- Determine the slope of the line in the graph and describe the slope in the words of the problem.
- If you don’t use your cell phone at all for the month of October, how much will you have to pay?
- Determine the equation of the line in the graph. Verify your answers from (b) and (d)
- Another company offers a cell phone plan that costs $20 per month and then charges $0.15 per Mb. Determine the cost equation and graph it using the same grid.
- If you use 175 Mb, which plan is cheaper and by how much?
- Use the equations to determine the number of Mb that result in the same cost for both plans.
2. Baby Sitters R Us charges a flat booking fee plus an hourly rate. On a normal workday, I hire a Sitter for 9 hours, and I pay $123.50. On Saturday night, I usually hire a sitter for 4 hours while I go to the movies, and I pay $66.
- Find a linear equation giving cost in terms of the number of hours.
- Describe the slope in the words of the problem.
- If I hire a sitter for 6 hours, how much will it cost me?
