Question

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The graph below shows the relationship between the number of months different students practiced tennis and the number of matches they won:


Part A: What is the approximate y-intercept of the line of best fit and what does it represent? (5 points)

Part B: Write the equation for the line of best fit in the slope-intercept form and use it to predict the number of matches that could be won after 13 months of practice. Show your work and include the points used to calculate the slope. (5 points)

Answer 1

Let's actually find the line of best fit...

m=(nΣyx-ΣyΣx)/(nΣx^2-ΣxΣx)

m=(11*836-130*55)/(11*385-3025)

m=2046/1210  

m=93/55

b=(Σy-93Σx/55)/n

b=(55Σy-93Σx)/(55n)

b=(7150-5115)/(55*11)

b=185/55, so the line of best fit is:

y=(93x+185)/55

A)  The approximate y-intercept (the value of y when x=0) is 185/55≈3.36.

Which means that those who do not practice at all will win about 3.36 times

B) y(13)=(93x+185)/55

y(13)≈25.34

So after 13 months of practice one would expect to win about 25.34 times.