This line can't be vertical, because it's impossible
#n -2 = n + 1 = 70#.
For non-vertical lines we use #f(x) = ax + b# three times, so that we can find #a(n), b(n), n#.
#n - 3 = a (n - 2) + b Rightarrow a = frac{n - 3 - b}{n - 2}# // Eq 1
#n + 9 = a(n+1) + b# // Eq 2
#n - 31 = 70a + b Rightarrow b = n - 31 - 70 cdot frac{n - 3 - b}{n - 2}#
We solve for b:
#b - (70b)/(n-2) = n - 31 - 70 cdot (n-3)/(n-2)# // times (n-2)
#b(n-2 -70) = n(n-2) -31(n-2) - 70(n - 3)#
#b(n) = frac{n^2 -103n + 272}{n - 72}#
From Eq. 1 #Rightarrow a = frac{n - 3 - frac{n^2 -103n + 272}{n - 72}}{n - 2}#
#a(n) = frac{n(n - 72) - 3(n - 72) -n^2 + 103n -272}{(n-2)(n-72)}#
Finally from Eq. 2,
#n+ 9 = frac{28n - 56}{(n-2)(n-72)} cdot (n + 1) + frac{n^2 -103n + 272}{n - 72}#
#Rightarrow n(n-72) + 9(n-72) = frac{28(n - 2)}{n-2} cdot (n + 1) + n^2 -103n + 272#
#Rightarrow n^2 - 72 n + 9n - 648 = n^2 -75n + 300#
#Rightarrow - 63 n - 648 = -75n + 300#
#Rightarrow (75- 63) n = 300 + 648#
