Section Exercises
Linear Equations
Use the following information to answer the next three exercises. A vacation resort rents SCUBA equipment to certified divers. The resort charges an up-front fee of $25 and another fee of $12.50 an hour.
1. What are the dependent and independent variables?
2. Find the equation that expresses the total fee in terms of the number of hours the equipment is rented.
3. Graph the equation from 2.
4. Find the equation that expresses the total fee in terms of the number of days the payment is late.
5. Graph the equation from 4.
6. Is the equation y = 10 + 5x – 3x2 linear? Why or why not?
7. Which of the following equations are linear?
a. y = 6x + 8
b. y + 7 = 3x
c. y – x = 8x2
d. 4y = 8
8. Does the graph show a linear equation? Why or why not?
The table below contains real data for the first two decades of AIDS reporting.
| Year | # AIDS cases diagnosed | # AIDS deaths |
| Pre-1981 | 91 | 29 |
| 1981 | 319 | 121 |
| 1982 | 1,170 | 453 |
| 1983 | 3,076 | 1,482 |
| 1984 | 6,240 | 3,466 |
| 1985 | 11,776 | 6,878 |
| 1986 | 19,032 | 11,987 |
| 1987 | 28,564 | 16,162 |
| 1988 | 35,447 | 20,868 |
| 1989 | 42,674 | 27,591 |
| 1990 | 48,634 | 31,335 |
| 1991 | 59,660 | 36,560 |
| 1992 | 78,530 | 41,055 |
| 1993 | 78,834 | 44,730 |
| 1994 | 71,874 | 49,095 |
| 1995 | 68,505 | 49,456 |
| 1996 | 59,347 | 38,510 |
| 1997 | 47,149 | 20,736 |
| 1998 | 38,393 | 19,005 |
| 1999 | 25,174 | 18,454 |
| 2000 | 25,522 | 17,347 |
| 2001 | 25,643 | 17,402 |
| 2002 | 26,464 | 16,371 |
| Total | 802,118 | 489,093 |
9. Use the columns “year” and “# AIDS cases diagnosed. Why is “year” the independent variable and “# AIDS cases diagnosed.” the dependent variable (instead of the reverse)?
Use the following information to answer the next two exercises. A specialty cleaning company charges an equipment fee and an hourly labor fee. A linear equation that expresses the total amount of the fee the company charges for each session is y = 50 + 100x.
10. What are the independent and dependent variables?
11. What is the y-intercept and what is the slope? Interpret them using complete sentences.
Use the following information to answer the next three questions. Due to erosion, a river shoreline is losing several thousand pounds of soil each year. A linear equation that expresses the total amount of soil lost per year is y = 12,000x.
12. What are the independent and dependent variables?
13. How many pounds of soil does the shoreline lose in a year?
14. What is the y-intercept? Interpret its meaning.
15. What are the slope and y-intercept? Interpret their meaning.
17. For each of the following situations, state the independent variable and the dependent variable.
- A study is done to determine if elderly drivers are involved in more motor vehicle fatalities than other drivers. The number of fatalities per 100,000 drivers is compared to the age of drivers.
- A study is done to determine if the weekly grocery bill changes based on the number of family members.
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