The equation of the line of fit is y = -0.8575x + 268.025. Describe how this relates to the winning times. The slope of the line means that for every year, the winning time Choose… by almost a full second. If this trend line continues, by the Olympics in 2048, the winning time should be about Choose… seconds.
The equation of the line of fit is y = -0.8575x + 268.025. Describe how this relates to the winning times. The slope of the line means that for every year, the winning time decreases by almost a full second. If this trend line continues, by the Olympics in 2048, the winning time should be about seconds.
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To analyze the equation of the line of fit, ( y = -0.8575x + 268.025 ), we can break this down step by step:
1. Understanding the slope: The slope of the line, -0.8575, indicates that for every additional year, the winning time decreases by approximately 0.8575 seconds. This means that over the years, winners are getting faster.
2. Calculating the estimated winning time for 2048:
– Assuming the current year is 2023, the number of years until 2048 is ( 2048 – 2023 = 25 ) years.
– We can plug this value into the equation to find the expected winning time. We will substitute ( x ) with 25 (assuming x = 0 is for the year 2023):
[
y = -0.8575(25) + 268.025
]
[
y = -21.4375 + 268.025
]
[
y = 246.5875 text{ seconds}
]
So, based on this trend, if it continues, by the Olympics in 2048, the winning time should be about 246.6 seconds (approximately 4 minutes and 6.6 seconds).
In summary, the slope indicates a trend of decreasing winning times, and the expected