Question
Question 1
(Multiple Choice Worth 5 Points)
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 35, 1 comma 39, 2 comma 32, 3 comma 24, 3 comma 30, 4 comma 20, 5 comma 18, 5 comma 22, 6 comma 4, 6 comma 14, 7 comma 8, and 8 comma 0, with a line passing through the coordinates 3 comma 25.2 and 7 comma 4.84
Find the y-intercept of the line of fit and explain its meaning in the context of the data.
The y-intercept is −5.1. The machine starts with 5.1 ounces of diet soda.
The y-intercept is 40.5. The machine starts with 40.5 ounces of diet soda.
The y-intercept is −5.1. The machine loses about 5.1 fluid ounces of diet soda each hour.
The y-intercept is 40.5. The machine loses about 40.5 fluid ounces of diet soda each hour.
(Multiple Choice Worth 5 Points)
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 35, 1 comma 39, 2 comma 32, 3 comma 24, 3 comma 30, 4 comma 20, 5 comma 18, 5 comma 22, 6 comma 4, 6 comma 14, 7 comma 8, and 8 comma 0, with a line passing through the coordinates 3 comma 25.2 and 7 comma 4.84
Find the y-intercept of the line of fit and explain its meaning in the context of the data.
The y-intercept is −5.1. The machine starts with 5.1 ounces of diet soda.
The y-intercept is 40.5. The machine starts with 40.5 ounces of diet soda.
The y-intercept is −5.1. The machine loses about 5.1 fluid ounces of diet soda each hour.
The y-intercept is 40.5. The machine loses about 40.5 fluid ounces of diet soda each hour.
Answers
GPT-4o mini
To find the y-intercept of the line of fit, we can analyze the trend of the data in relation to the x and y axes in the context of the problem. The y-intercept is the value of y when x = 0, representing the starting amount of diet soda in the machine when the time (x) is zero.
Given the options provided:
1. "The y-intercept is −5.1. The machine starts with 5.1 ounces of diet soda."
2. "The y-intercept is 40.5. The machine starts with 40.5 ounces of diet soda."
3. "The y-intercept is −5.1. The machine loses about 5.1 fluid ounces of diet soda each hour."
4. "The y-intercept is 40.5. The machine loses about 40.5 fluid ounces of diet soda each hour."
Since y represents the amount of diet soda remaining, a positive y-intercept signifies the initial amount of soda when the machine is filled, which can't be negative. Thus, the correct interpretation is likely option 2.
The answer should be:
**The y-intercept is 40.5. The machine starts with 40.5 ounces of diet soda.**
Given the options provided:
1. "The y-intercept is −5.1. The machine starts with 5.1 ounces of diet soda."
2. "The y-intercept is 40.5. The machine starts with 40.5 ounces of diet soda."
3. "The y-intercept is −5.1. The machine loses about 5.1 fluid ounces of diet soda each hour."
4. "The y-intercept is 40.5. The machine loses about 40.5 fluid ounces of diet soda each hour."
Since y represents the amount of diet soda remaining, a positive y-intercept signifies the initial amount of soda when the machine is filled, which can't be negative. Thus, the correct interpretation is likely option 2.
The answer should be:
**The y-intercept is 40.5. The machine starts with 40.5 ounces of diet soda.**