To determine the appropriate line of best fit from the given choices, let's interpret the results of the linear regression analysis shown in the table.
The standard form of a linear equation is given by [tex]\(y = ax + b\)[/tex], where:
- [tex]\(a\)[/tex] is the slope of the line,
- [tex]\(b\)[/tex] is the y-intercept (the value of [tex]\(y\)[/tex] when [tex]\(x = 0\)[/tex]).
From the results of the linear regression:
- The slope ([tex]\(a\)[/tex]) is -2.9.
- The y-intercept ([tex]\(b\)[/tex]) is 13.5.
Using these values, the equation of the line of best fit can be written as:
[tex]\[ y = -2.9x + 13.5 \][/tex]
Now let's match this equation with the provided options:
A. [tex]\(-0.984 = -2.9x + 13.5\)[/tex] (This does not match the form [tex]\(y = ax + b\)[/tex])
B. [tex]\(y = -2.9x + 13.5\)[/tex] (This matches the form [tex]\(y = ax + b\)[/tex])
C. [tex]\(y = 13.5x - 2.9\)[/tex] (This has the slope and y-intercept reversed)
D. [tex]\(y = -0.984x + 13.5\)[/tex] (This has an incorrect slope)
The correct equation of the line of best fit is given by option B:
[tex]\[ y = -2.9x + 13.5 \][/tex]
So, the line of best fit is:
[tex]\[ \boxed{y = -2.9x + 13.5} \][/tex]
