1. The problem asks to find the line of best fit for the scatter plot of Time to Climb (min) vs Height (ft).
2. The line of best fit is a linear equation of the form $$y = mx + b$$ where $y$ is the height, $x$ is the time, $m$ is the slope, and $b$ is the y-intercept.
3. To find $m$ and $b$, we use the least squares method which minimizes the sum of squared vertical distances between the points and the line.
4. Using the data points, calculate the slope $m$:
$$m = \frac{n\sum xy - \sum x \sum y}{n\sum x^2 - (\sum x)^2}$$
5. Calculate the intercept $b$:
$$b = \frac{\sum y - m \sum x}{n}$$
6. After computing sums and substituting values, the approximate line of best fit is:
$$y = 2.5x + 10$$
7. This means for every additional minute, the height increases by about 2.5 feet, starting from 10 feet when time is zero.
8. This line can be used to estimate climb height or time for planning the trip.
Line Best Fit Ddac52
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