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A swim coach gave the table of goal times for the 50-meter freestyle to a team of swimmers. Using the ages 12 and 18, what is the equation of the line of fit for this data? Age Time (s)10 44.0912 38.3914 37.0916 36.3918 36.17

Question

A swim coach gave the table of goal times for the 50-meter freestyle to a team of swimmers. Using the ages 12 and 18, what is the equation of the line of fit for this data? Age Time (s)10 44.0912 38.3914 37.0916 36.3918 36.17

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Solution

I'm sorry, but you didn't provide a specific question. Are you asking how to find the equation of the line of fit for the given data? If so, here are the steps:

  1. First, we need to find the slope of the line. The slope (m) is given by the formula: m = (y2 - y1) / (x2 - x1). Here, x and y are the coordinates of two points on the line. We can use the ages 12 and 18 as x1 and x2, and the corresponding times as y1 and y2. So, m = (36.17 - 38.39) / (18 - 12) = -2.22 / 6 = -0.37.

  2. Next, we need to find the y-intercept (b). We can use the formula: b = y - mx, where x and y are the coordinates of any point on the line. We can use the point (12, 38.39) for this. So, b = 38.39 - (-0.37 * 12) = 38.39 + 4.44 = 42.83.

  3. Therefore, the equation of the line of fit for this data is y = -0.37x + 42.83.

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