To determine the approximate slope of the line of best fit for the given data, we start by noting the pairs of values:
- Hours: [tex]\([1, 2, 3, 4, 5, 6, 7, 8]\)[/tex]
- Errors: [tex]\([36, 34, 30, 31, 23, 16, 11, 5]\)[/tex]
A best-fit line seeks to minimize the differences between the actual data points and the line predicted by a linear model. This linear model can be expressed by the equation of a line: [tex]\(y = mx + b\)[/tex], where [tex]\(m\)[/tex] is the slope and [tex]\(b\)[/tex] is the y-intercept.
The slope of the line of best fit can be mathematically determined, and it represents the average rate of change in the number of errors for each additional hour of practice. Given the options provided, we compare our calculations to identify the most accurate one.
After careful computation, the approximate slope of the line of best fit for the provided data is determined to be:
[tex]\[
\boxed{-4.5}
\][/tex]
This indicates that on average, each additional hour of practice results in approximately 4.5 fewer errors.
