Let the given points be A(3, 0), B(–2, –2) and C(8, 2). Then the equation of the line passing through A and B is

y−0

x−3

=

−2−0

−2−3

⇒

y

x−3

=

−2

−5

⇒ 5y = 2x - 6
Clearly the point C(8, 2) satisfy the equation 2x – 5y – 6 = 0.
(Since 2(8) – 5(2) – 6 = 16 – 10 – 6 = 0)
Hence, the given points lie on the same straight line whose equation is 2x – 5y – 6 = 0.