Find x such that the following points are collinear:

(2, -6), (-1, x), and (7, 4)

x=

Three points (x_{1}, y_{1}), (x_{2},
y_{2}), and (x_{3}, y_{3}) are collinear (lie on the
same line) if and only if

Therefore, if we want the points (2, -6), (-1, x), and (7, 4) to be collinear – we must have

0=-60-5x

60=-5x

60/-5=x

-12=x

The points (2, -6), (-1, -12), and (7, 4) are collinear.