Point $P (7, 5)$ divides the line segment between the axes in the ratio $2 : 3$ . Find the equation of the line .

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Solution

$\begin{matrix} m_{1} = 2 m_{2} = 3 (x_{1}, y_{1}) = (9, 0) (x_{1}, y_{2}) = (0, b) p (7, 5) = [\frac{m_{1} x_{2} + m_{2} x_{1}}{m_{1} + m_{2}}, \frac{m_{1} y_{2} + m_{2} y_{1}}{m_{1} + m_{2}}] p (7, 5) = [\frac{2 \times 0 + 3 a}{5}, \frac{2 \times b + 3 \times 0}{5}] 7 = \frac{3 a}{5} 5 = \frac{2 b}{5} a = \frac{35}{3} & b = \frac{25}{2} e q u a t i o n \frac{x}{a} + \frac{y}{b} = 1 \frac{x}{35 / 3} + \frac{y}{25 / 2} = 1 \frac{3 x}{35} + \frac{2 y}{25} = 1 \frac{15 x + 14 y}{175} = 1 15 x + 14 y = 175 \end{matrix}$

Hence, this is the answer.

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