We can use the fact that, for
,

Notice that
![\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1{1-x}\right]=\dfrac1{(1-x)^2}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cleft%5B%5Cdfrac1%7B1-x%7D%5Cright%5D%3D%5Cdfrac1%7B%281-x%29%5E2%7D)
so that
![f(x)=\displaystyle\frac5{(1-x)^2}=5\frac{\mathrm d}{\mathrm dx}\left[\sum_{n=0}^\infty x^n\right]](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdisplaystyle%5Cfrac5%7B%281-x%29%5E2%7D%3D5%5Cfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cleft%5B%5Csum_%7Bn%3D0%7D%5E%5Cinfty%20x%5En%5Cright%5D)



By the ratio test, this series converges if

so the series has radius of convergence
.
If R represents Reggie's time, the total time for the team is
.. R +(R +2.45) +(R -3.81) = 3R -1.36
.. = 3*57.12 -1.36
.. = 170.00 . . . seconds
The answer is -7 because if you subtract the first equation by the second equation then you’ll find the y-coordinate: 12. You use the second equation to find the x-coordinate.
First, solve for slope.
Formula for slope:

Plug in values:

Slope:

Second, we must plug into point-slope form.
Formula for point-slope:

Plug in the values:

And there you have your answer in point-slope form