The points (2,-3), (3,-2) & (8,k) lie on a straight line. Find k.

If the given points are located on the same line, the
value of the determinant formed by the coordinates of 3 points has to be
zero:

                         2    -3   
1

determinant =   3    -2   
1

                          8     k    
1

We'll calculate the
determinant:

det. = (2*-2*1) + 3*k*1 + 1*8*(-3) - (-2)*1*8
- 2*k - (-3)*3*1

det. = -4 + 3k - 24 + 16 - 2k +
9

But the determinant has to be equal to zero, if the
points are on the line.

 -4 + 3k - 24 + 16 - 2k + 9 =
0

We'll combine like terms:

k
- 3 = 0

k =
3