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$\mathrm{a}$ and $\mathrm{b}$ are the intercepts made by a line on the co-ordinate axes. If $3 \mathrm{a}=\mathrm{b}$ and the line passes through $(1,3)$, then the equation of the line is
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Verified Answer
The correct answer is:
$3 x+y=6$
Let the equation of the line be
$$
\frac{x}{\mathrm{a}}+\frac{y}{\mathrm{~b}}=1
$$
This line passes through the point $(1,3)$
$$
\begin{aligned}
\therefore \quad & \frac{1}{a}+\frac{3}{b}=1 \\
& \Rightarrow b+3 a=a b \\
& \Rightarrow 2 b=a b \\
& \Rightarrow a=2 \\
\therefore \quad & b=3 a=6
\end{aligned}
$$
Equation (i) becomes,
$$
\begin{aligned}
& \frac{x}{2}+\frac{y}{6}=1 \\
& 3 x+y=6
\end{aligned}
$$
$$
\frac{x}{\mathrm{a}}+\frac{y}{\mathrm{~b}}=1
$$
This line passes through the point $(1,3)$
$$
\begin{aligned}
\therefore \quad & \frac{1}{a}+\frac{3}{b}=1 \\
& \Rightarrow b+3 a=a b \\
& \Rightarrow 2 b=a b \\
& \Rightarrow a=2 \\
\therefore \quad & b=3 a=6
\end{aligned}
$$
Equation (i) becomes,
$$
\begin{aligned}
& \frac{x}{2}+\frac{y}{6}=1 \\
& 3 x+y=6
\end{aligned}
$$
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