Question

A line passes through (6,3), (8,4), and (n,-2). Find the value of n.

Answer 1

If a line pass through three points, they are collinear points, and the determinant of a matrix produced by their coordinates equals 0.

Knowing this, we can fin the value of n.

We need a triangular matrix, so we can complete it with 1's.

$\left[\begin{array}{ccc}6&3&1\\8&4&1\\n&-2&1\end{array}\right]$

24 + 3n - 16 - 4n + 12 - 24 = 0

- n - 4 = 0

- n = 4

n = -4

The value of n it's -4.

Hope it helps.

Answer 2

-1
because there is a pattern..
6 / 2 = 3
8 / 2 = 4
 -2 / 2 = -1