Linear Relationships (Hard)

A gym charges a one-time registration fee and then $25 per month. After 6 months, a customer has paid $205 in total. Write a linear model for total cost (C) in terms of months (m), and find the registration fee.

• C = 25m + 50; registration fee = $50

• C = 30m + 25; registration fee = $25

• C = 25m + 30; registration fee = $30

• C = 20m + 55; registration fee = $55

The function P(t) = 1250 + 43t models the number of books sold t years after 1997. Given that P(18) = 1974, what does the constant term 1250 represent in this model?

• Books sold 18 years after 1997

• Initial number of books sold in 1997

• Increase in books sold per year

• Total books sold over 18 years

A worker paints fences at a constant rate. After painting 3 fences, he has worked for 4 hours. After 9 fences, he has worked 10 hours. Create a linear model to represent time (t) as a function of fences painted (f). How long will it take to paint 15 fences?

• t = f + 2; 17 hours

• t = f + 1; 16 hours

• t = f + 3; 18 hours

• t = f + 0.5; 15.5 hours

A repair technician charges $80 for the first hour, which includes a $20 travel fee. Each additional hour costs $60. What is the linear model for total cost (C) after h hours of work (where h ≥ 1)?

• C = 80h + 20

• C = 60(h – 1) + 80

• C = 60h + 20

• C = 60h + 80

A bus starts with 40 passengers. At every stop, 8 passengers get off. If there are s stops, write a linear equation for the number of passengers left (P), and find how many are left after 7 stops.

• P = 40 – 8s;

  8 passengers

• P = –8s + 48;

  0 passengers

• P = 8s – 40;

  16 passengers

• P = 40 – 8s;

  16 passengers

A phone plan offers 2 GB of free data. After that, users pay $10 per additional GB used. If a user pays $80 in a month, how many total GBs did they use?

• 12

• 6

• 8

• 10

A line has the equation . It passes through the points (0, 1) and (5, 11).What is the value of a + b?

A hiker began climbing a mountain trail at 9:00 a.m. and reached the 7-mile mark at 11:30 a.m. She continued hiking at the same pace and finished the full 11-mile trail. At what time did she finish?

• 1:30 p.m.

• 1:00 p.m.

• 12:45 p.m.

• 12:30 p.m.

The function R(t)=860+55t shows the revenue (in thousands of dollars) of a startup t years after it is

launched in 2005. It is given that R(10) = 1410.What does the value 1410 mean here?

• Initial revenue

• Revenue in 2015

• Total revenue increase over 10 years

• Average yearly revenue

A line passes through (–2, 3) and (4, y). If the average of the y-values of the two points is 7, find the equation of the line.

• y = (1/2)x + 5
• y = (3/4)x + 6
• y = (2/3)x + 4
• y = (4/3)x + (17/3)