Question

a local store ordered a shipment of video game systems. the store sells 60 systems weekly to customers. as a result, the number of systems in stock decreased to 230 in the first week. which statements correctly interpret the rate of change, or the y - intercept, of the given situation? select two answer choices.

a. there are 60 systems sold each week.

b. there are 230 systems sold each week.

c. there are 290 systems in the shipment.

d. the situation can be modeled as $y = 60x - 230$.

e. the situation can be modeled as $y = -60x + 290$.

Explanation:

Step1: Define variables and linear model

Let \(x\) = weeks, \(y\) = stock. Rate of change = -60 (weekly sales). After 1 week (\(x=1\)), \(y=230\). Use \(y = mx + b\): \(230 = -60(1) + b\).

Step2: Calculate y-intercept (initial stock)

Solve for \(b\): \(b = 230 + 60 = 290\). So model is \(y = -60x + 290\).

Step3: Evaluate options

• A: Correct (rate of change = 60 sold/week).
• B: Incorrect (230 is week 1 stock).
• C: Correct (y-intercept = initial shipment = 290).
• D: Incorrect (model sign wrong).
• E: Correct model, but question needs two choices (A and C are interpretations of rate/y-intercept).

Answer:

A. There are 60 systems sold each week, C. There are 290 systems in the shipment.