Find the equation of the line which passes through the point (22, -6) and whose intercept on the x-axis exceeds the intercept on the y-axis by 5.
To Find:The equation of the line that passes through the point (22, -6) and intercepts on the x-axis exceeds the intercept on the y-axis by 5.
Given : let x-intercept be a and y-intercept be b.
According to the question : a = b + 5
Formula used:
And the given point satisfies the equation of the line, so
= 1
= 1
22b – 6b -30 = b2 + 5b
11b – 30 = b2
b2 -11b +30 = 0
b2 -6b -5b +30 =0
b(b-6) -5(b-6) =0
(b-5) (b-6) =0
The values are b=5 ,b=6
When b=5 then a=10
and b=6 then a=11
case 1 : when b=5 and a=10
Equation of the line : 
= 1
= 1
= 1
Hence, x + 2y = 10 is the required equation of the line.
case 2 : when b=6 and a=11
Equation of the line : 
= 1
= 1
= 1
Hence, 6x + 11y = 66 is the required equation of the line.
Therefore, x + 2y = 10 is the required equation of the line when b=5 and a=10 .And 6x + 11y = 66 is the required equation of the line when b=6 and a=11.