Comparing Initial Values in Linear Functions

Kyle sells bags of popcorn at school events. The function P = 1.25b – 18 represents Kyle’s profit, where P stands for profit and b stands for the number of bags of popcorn sold. His brother Nathan sells bottles of fruit juice and has kept track of his daily sales and profit in the table. If Nathan’s profit is modeled linearly, which statement can be predicted from the two models?

• Kyle will have a higher profit than Nathan if they each sell 50 items.

• Kyle will have a higher profit than Nathan if they each sell 40 items.

• Kyle will have a higher profit than Nathan if they each sell 30 items.

• Kyle will have a higher profit than Nathan if they each sell 20 items.

Allison compared the y-intercept of f(x)= 4 – 5x to the y-intercept of the function that fits the values in the table.

Which statement is true?

• The y-intercept of g(x) is half the y-intercept of f(x).

• The y-intercept of g(x) is two times the y-intercept of f(x).

• The y-intercept of g(x) is equal to the y-intercept of f(x).

• The y-intercept of g(x) is the negative value of the y-intercept of f(x).

How far is the y-intercept of the function that fits the values in the table, from the y-intercept of the function graphed?

• 1 unit

• 2 units

• 5 units

• 9 units

Angela earns $8 for every hour she works at her job. The amount of money Kelly earns at her job is modeled by the function f(x) = 15t, where t represents hours worked. Angela and Kelly both worked 38 hours last week. Which statement accurately describes the amount of money Angela and Kelly earned last week?

• Angela made $38 more than Kelly.

• Kelly made $266 more than Angela.

• Angela made $304 more than Kelly.

• Kelly made $570 more than Angela.

Jason invested money into two different accounts. He deposited $75 into the first account which earns 6% interest annually. The value of the second account after different amounts of time is shown in the table.

Which statement is true?

• Jason started with $4 less in the second account than the first account.

• Jason started with $5 less in the second account than the first account.

• Jason started with $4 more in the second account than the first account.

• Jason started with $5 more in the second account than the first account.

The cost of Nate’s service is described by y = 4x + 6. The table shows the cost of Beth’s service. Which service is cheaper for renting 9 movies?

• Beth's service is cheaper (Beth charges $42 vs. Nate charges $45)

• Nate’s service is cheaper (Nate charges $42 vs. Beth charges $45) 

• Nate’s service is cheaper (Nate charges $36 vs. Beth charges $45)

• Beth's service is cheaper (Nate charges $45 while she charges $36) 

Which company shows a greater rate of change?

• Water's Edge Rafts

• Ryan's Rafts

Which company should you use if you rent the raft for 9 hours?

• Water's Edge Rafts

• Ryan's Rafts

Who weighed more at the beginning of the show?

• Valerie

• Oscar

• Mrs. Conte

• They weighed the same

Who is losing weight faster?

• Valerie

• Oscar

• Mrs. Conte

• They are losing the same amount of weight