To determine the approximate slope of the line of best fit for the provided data, we'll follow these steps:
1. Collect the Data:
- Number of hours practiced, [tex]\( x \)[/tex]: [tex]\( [1, 2, 3, 4, 5, 6, 7, 8] \)[/tex]
- Number of errors made, [tex]\( y \)[/tex]: [tex]\( [36, 34, 30, 31, 23, 16, 11, 5] \)[/tex]
2. Understand the Slope of the Line:
The slope (denoted as [tex]\( m \)[/tex]) of the line of best fit indicates the rate of change in the number of errors for each additional hour of practice. Mathematically, this is often computed using methods like linear regression.
3. Interpreting the Slope:
After performing the necessary calculations (which we assume to have been conducted accurately), the slope [tex]\( m \)[/tex] is found to be approximately -4.5476. This means that for each additional hour of practice, the number of errors made decreases by about 4.5476.
4. Selecting the Closest Approximation:
Given this slope, we compare it to the provided choices:
- [tex]$-5.5$[/tex]
- [tex]$-4.5$[/tex]
- [tex]$-2.0$[/tex]
- [tex]$-1.0$[/tex]
The closest value to -4.5476 is [tex]\( -4.5 \)[/tex].
5. Conclusion:
Therefore, the approximate slope of the line of best fit for this dataset is [tex]\( -4.5 \)[/tex].
So, the correct answer is:
[tex]\[ \boxed{-4.5} \][/tex]
