(2,3), (3,-2) and (8,k). find k

What is your question?

Let's
suppose that you want to determine k when the points are on the same
line.

First, we'll determine the line taht is passing
through the points (2,3) and (3,-2):

y = ax +
b

If (2,3) is on the line, then it's coordinates verify the
equation of the line:

3 = 2a + b => b = 3 - 2a
(1)

If (3,-2) is on the line, then it's coordinates verify
the equation of the line:

-2 = 3a + b
(2)

We'll substitute (1) in (2) and we'll
get:

-2 = 3a + 3 - 2a

-2 - 3 =
3a - 2a

-5 = a

a =
-5

b = 3 - 2a => b = 3 + 10 =
13

The equation of the line that is passing through (2,3)
and (3,-2) is:

y = -5x +
13

Now, we'll impose the constraint that this line to pass
through the point (8,k), too:

k = -5*8 +
13

k = -40 + 13

k =
-27

The line is passing through all these
given points, for k = -27.