To determine the line of best fit from the results provided by the linear regression, we need to understand the following equation format for a linear relationship:
[tex]\[ y = ax + b \][/tex]
Where:
- [tex]\( a \)[/tex] is the slope of the line.
- [tex]\( b \)[/tex] is the y-intercept.
Given the results from the linear regression:
- [tex]\( a = -3.6 \)[/tex]
- [tex]\( b = 12.8 \)[/tex]
We can plug these values into the linear equation format to get the line of best fit:
[tex]\[ y = -3.6x + 12.8 \][/tex]
Now, let's compare this line of best fit with the options provided:
A. [tex]\( y = 12.8x - 3.6 \)[/tex]
This option is not correct because it incorrectly switches the values of [tex]\( a \)[/tex] and [tex]\( b \)[/tex].
B. [tex]\( y = -3.6x + 12.8 \)[/tex]
This option is correct as it matches our calculated line of best fit.
C. [tex]\( y = -0.998x + 12.8 \)[/tex]
This option is not correct because it has the incorrect slope ([tex]\( a \)[/tex]) value.
D. [tex]\( -0.998 = -3.6x + 12.8 \)[/tex]
This option is not correctly formatted as an equation of a line in the [tex]\( y = ax + b \)[/tex] form.
Therefore, the correct option is:
B. [tex]\( y = -3.6x + 12.8 \)[/tex]
