Given the table data and using the method of the line of best fit, we can derive the equation of the line that best matches the data points.
1. First, we determine the slope [tex]\(m\)[/tex] and the y-intercept [tex]\(b\)[/tex] of the line of best fit using the least squares method.
The slope ([tex]\(m\)[/tex]) and y-intercept ([tex]\(b\)[/tex]) are calculated as follows:
- [tex]\(m = 1.06\)[/tex]
- [tex]\(b = -6.00\)[/tex]
Therefore, the equation of the line of best fit is:
[tex]\[
y = 1.06x - 6
\][/tex]
2. Next, to predict the number of games won if the chess player plays 40 games, we substitute [tex]\(x = 40\)[/tex] into the equation of the line:
[tex]\[
y = 1.06(40) - 6
\][/tex]
[tex]\[
y = 42.4 - 6
\][/tex]
[tex]\[
y = 36.4
\][/tex]
So, based on the table data and the line of best fit:
- The line of best fit for the situation is [tex]\(y = 1.06x - 6\)[/tex].
- If the chess player plays 40 games in the next competition, the expected number of games won would be approximately 36.4.
Therefore, the completed statement is:
The line of best fit for the situation is [tex]\(y = 1.06x - 6\)[/tex]. If the chess player plays 40 games in the next competition, the expected number of games won would be approximately 36.4.
