Let A(2,-3) B(3,-2) and C(8,k) lie on a straight line

Then, the slope for BC (m1) = the slope for AC (m2

Let us calculate:

m1= k+3)/(8-2) = (k+3)/6

m2 = (k+2)/(8-3) = (k+2)/5

m1 = m2

==> (k+3)/6 = (k+2)/5

Cross multiply:

==> 5(k+3) = 6(k+2)

==> 5k + 15 = 6k+ 12

==> 15-12 = 6k - 5k

==> k = 3