First slide

Equation of line in Straight lines

Question

The portion of a line intercepted between the coordinate axes is divided by the point $(2, 2)$ in the ratio 3: 2. The equation of the line is

Moderate

A

$x + y = 10$
B

$2 x + 3 y = 10$
C

$x - 2 y = 5$
D

$4 x + y = 3$

Solution

Let $A (a, 0)$ , $B (0, b)$
$∴ (2, 2) = (\frac{2 a}{5}, \frac{3 b}{5})$
$∴ a = 5, b = \frac{10}{3}$
$∴$ The equation is $\frac{x}{5} + \frac{y}{10 / 3} = 1$
$\frac{x}{5} + \frac{3 y}{10} = 1 \frac{2 x + 3 y}{10} = 1$

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