Question

A movie theater wanted to determine the average rate that their diet soda is purchased. An employee gathered data on the amount of diet soda remaining in the machine, y, for several hours after the machine is filled, x. The following scatter plot and line of fit was created to display the data.

scatter plot titled soda machine with the x axis labeled time in hours and the y axis labeled amount of diet soda in fluid ounces, with points at 1 comma 32, 1 comma 40, 2 comma 35, 3 comma 20, 3 comma 32, 4 comma 20, 5 comma 15, 5 comma 25, 6 comma 10, 6 comma 22, 7 comma 12, and 8 comma 0, with a line passing through the coordinates 2 comma 32.1 and 7 comma 9.45

Find the y-intercept of the line of fit and explain its meaning in the context of the data.

The y-intercept is 41.16. The machine starts with 41.16 ounces of diet soda.
The y-intercept is 41.16. The machine loses about 41.16 fluid ounces of diet soda each hour.
The y-intercept is −4.5. The machine starts with 4.5 ounces of diet soda.
The y-intercept is −4.5. The machine loses about 4.5 fluid ounces of diet soda each hour.

Answer 1

Explanation:

The y-intercept of the line of fit is 41.16, which means that when the machine is first filled, it starts with approximately 41.16 fluid ounces of diet soda.

In the context of the data, the y-intercept represents the initial amount of diet soda in the machine before any soda is purchased. This information can be useful for determining how much soda is being purchased by customers over time, as it provides a baseline for comparison.

Therefore, the correct answer is: The y-intercept is 41.16. The machine starts with 41.16 ounces of diet soda.

Answer 2

y-intercept is 41.16. The machine starts with 41.16 ounces of diet soda.

Explanation: