To find the correct linear function that models the height of the candle (y) based on the number of minutes it has burned (x), we can analyze the data provided:
From the data:
- When x = 1, y = 8,000
- When x = 2, y = 6,000
- When x = 3, y = 4,000
- When x = 4, y = 2,000
- When x = 5, y = 0
From the observations, we can determine that the height decreases by 2,000 mm for each additional minute burned. The slope of the function (the rate of change) is -2,000 mm per minute.
Next, we need to find the y-intercept. When the candle has burned for 0 minutes (x = 0), its height starts at 10,000 mm. Thus, when x = 0, y = 10,000.
Now we can write the linear equation in the form y = mx + b, where m is the slope and b is the y-intercept:
- Slope (m) = -2,000
- y-intercept (b) = 10,000
Thus, the function is: \[ y = -2,000x + 10,000 \]
Referring to the provided options, the correct answer is:
D) y = -2,000x + 10,000