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1. ⇒ (MHT CET 2023 11th May Morning Shift )

$a$ and $b$ are the intercepts made by a line on the co-ordinate axes. If $3 a = b$ and the line passes through $(1, 3)$ , then the equation of the line is

A. $x + 3 y = 10$

B. $3 x + y = 6$

C. $x - 3 y + 8 = 0$

D. $3 x - 2 y + 3 = 0$

Correct answer option is (B)

Let the equation of the line be

$\frac{x}{a} + \frac{y}{b} = 1$ .... (i)

This line passes through the point $(1, 3)$

$\begin{aligned} ∴ & \frac{1}{a} + \frac{3}{b} = 1 \\ \Rightarrow b + 3 a = a b \\ \Rightarrow 2 b = a b . . . [∵ 3 a = b] \\ \Rightarrow a = 2 \\ ∴ & b = 3 a = 6 \end{aligned}$

Equation (i) becomes,

$\begin{aligned} \frac{x}{2} + \frac{y}{6} = 1 \\ 3 x + y = 6 \end{aligned}$

⇒Straight Line