Question

Question 5
(Multiple Choice Worth 2 Points)
(Graphing Linear Equations MC)

A eyeglasses store is checking their inventory. The table shows the relationship between the number of days since the opening of the eyeglasses store and the total amount of sunglasses in their inventory.

Sunglasses Inventory
Number of Days Total Amount of Sunglasses
2 52
5 46
7 42
10 36


Which graph shows the relationship given in the table?
graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 62 through the point 1 comma 60
graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 56 through the point 1 comma 54
graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 58 through the point 1 comma 56
graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 52 through the point 1 comma 50

Answer 1

To determine the correct graph that represents the inventory data, we need to analyze the pattern in the table provided:

- At 2 days, the total amount of sunglasses is 52.
- At 5 days, the total amount is 46.
- At 7 days, the total amount is 42.
- At 10 days, the total amount is 36.

We can calculate the rates of change in sunglasses inventory over the specified days:

1. From day 2 to day 5:
- 52 - 46 = 6 sunglasses decrease over 3 days.
- Rate of decrease = 6 / 3 = 2 sunglasses per day.

2. From day 5 to day 7:
- 46 - 42 = 4 sunglasses decrease over 2 days.
- Rate of decrease = 4 / 2 = 2 sunglasses per day.

3. From day 7 to day 10:
- 42 - 36 = 6 sunglasses decrease over 3 days.
- Rate of decrease = 6 / 3 = 2 sunglasses per day.

The inventory seems to decrease consistently by 2 sunglasses per day. This suggests a linear relationship.

Next, we need to check the y-intercept, which would be the estimated initial amount of sunglasses. From the pattern, we can find the y-intercept by extending the line backward to when days equal 0.

Since at day 2, the inventory is 52, we would estimate the intercept:

- Going back 2 days at a rate of 2 sunglasses per day:
- 52 + 2*2 = 52 + 4 = 56.

So we can infer that at day 0, the estimated amount of sunglasses would be approximately 56.

Based on this analysis, the graph with a y-intercept around 56 and a slope that indicates a decrease of 2 sunglasses per day should be the correct representation. Therefore, the correct graph is:

**Graph with the x-axis labeled number of days and the y-axis labeled total amount of sunglasses and a line going from the point (0, 56) through the point (1, 54).**