Question

If the line `x/"a" + y/"b"` = 1 passes through the points (2, –3) and (4, –5), then (a, b) is ______.

Options

• (1, 1)

• (– 1, 1)

• (1, – 1)

• (– 1, –1)

Answer 1

If the line `x/"a" + y/"b"` = 1 passes through the points (2, –3) and (4, –5), then (a, b) is (– 1, –1).

Explanation:

Equation of line passing through the points (2, – 3) and (4, – 5) is y + 3 = `(-5 + 3)/(4 - 2) (x - 2)`

⇒ y + 3 = `(-2)/2 (x - 2)`

⇒ y + 3 = – (x – 2)

⇒ y + 3 = – x + 2

⇒ x + y = – 1

⇒ `x/(-1) + y/(-1)` = 1   (Intercept form)

∴ a = – 1, b = – 1