If the points (1, 4), (3, -2) and (p, -5) lie on a line, find the value of p.

Equation of line passing through (1, 4) and (3, -2) i.e two points can be given by two-point formula i.e. Since (p, -5) lies on the line it will satisfy it. Putting the values, ⇒ -5 = -3p + 7 ⇒ 3p = 7 + 5 ⇒ 3p = 12 ⇒ p = 4. Hence, the value of p is 4.