Find the equation of the line passing through (22, –6) and having intercept on x–axis exceeds the intercept on y–axis by 5.

Let the x intercept be ‘a’. It is given that x intercept exceeds the y intercept by 5

⇒ y intercept = a– 5

The equation of the line using the intercept form is

Substituting Value of b

⇒ x (a–5) + ya = a(a–5)

Given that the point (22, –6) lies on this equation of the line, hence it should satisfy it

22(a–5) + (–6) a = a(a–5)

⇒ 22a – 110 – 6a = a² –5a

⇒ a² – 21a + 110 = 0

⇒ a(a–10) – 11(a –10) = 0

⇒ (a–11) (a–10)

⇒ a = 11 or 10

The equation of the line is

x(11–5) + 11y = 11(11–5)

⇒ 6x + 11y – 66 = 0

Or

x(10–5) + 10y = 10(10–5)

⇒ 5x + 10y– 50 = 0

⇒ x + 2y –10 = 0