12.1 Linear Equations

A local small business completes federal tax returns for customers. The rate for services is $32 per hour plus a $31.50 one-time charge. The total cost to a customer depends on the number of hours it takes to complete the job.

Find the equation that expresses the total cost in terms of the number of hours required to complete the job.

Svetlana tutors to make extra money for college. For each tutoring session, she charges a one-time fee of $25 plus $15 per hour of tutoring. A linear equation that expresses the total amount of money Svetlana earns for each session she tutors is y = 25 + 15x.

What are the independent and dependent variables? What is the y-intercept and what is the slope? Interpret them using complete sentences.

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.

What are the dependent and independent variables?

Use the following information to answer the next two exercises. A credit card company charges $10 when a payment is late, and $5 a day each day the payment remains unpaid.

Which of the following equations are linear?

a. y = 6x + 8

b. y + 7 = 3x

c. y – x = 8x²

d. 4y = 8

Use the columns "year" and "# flu cases diagnosed. Why is “year” the independent variable and “# flu 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.

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.

How many pounds of soil does the shoreline lose in a year?

Use the following information to answer the next two exercises. The price of a single issue of stock can fluctuate throughout the day. A linear equation that represents the price of stock for Shipment Express is y = 15 – 1.5x where x is the number of hours passed in an eight-hour day of trading.

What are the slope and y-intercept? Interpret their meaning.

For each of the following situations, state the independent variable and the dependent variable.

1. 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.
2. A study is done to determine if the weekly grocery bill changes based on the number of family members.
3. Insur…