Question

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.

Answer 1

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

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

Hence, x + 2y = 10 is the required equation of the line.

case 2: when b = 6 and a = 11

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.