The rate of change for the line of best fit = -2.5 degrees
What is rate of change?
"The rate at which one quantity is changing with respect to another quantity."
What is the equation of the line passing through two points?
"The equation of the line passing through points [tex](x_1,y_1),(x_2,y_2)[/tex] is [tex]\frac{y-y_1}{y_2-y_1}= \frac{x-x_1}{x_2-x_1}[/tex]"
For given question,
We have been given a scatter plot and the line of best fit.
We can observe that the line of best fit passes through points (40, 25) and (30, 50)
Let [tex](x_1,y_1)=(30,50),(x_2,y_2)=(40,25)[/tex]
So, the equation of the line of best fit would be,
[tex]\Rightarrow \frac{y-50}{25-50}= \frac{x-30}{40-30} \\\\\Rightarrow \frac{y-50}{-25}= \frac{x-30}{40-3010} \\\\\Rightarrow y-50=\frac{-25}{10} (x-30)\\\\\Rightarrow y-50=-2.5x+75\\\\\Rightarrow y=-2.5x+125[/tex]
Here slope of the line is [tex]m=-2.5[/tex]
We know that the slope is the rate of change for the line of best fit.
Therefore, the rate of change for the line of best fit = -2.5 degrees
Learn more about the rate of change here:
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