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JEE Main 201322 AprilOnline

Exam: JEE Main
Year: 2013
Date: 22 April
Mode: Online
Subject: Mathematics
Chapter: Straight Lines

JEE Main 2013 · 22 April · Online · Mathematics · Straight Lines

If the x -intercept of some line L is double as that of the line, 3...

If the

x

-intercept of some line

L

is double as that of the line,

3 x+4 y=12

and the

y

-intercept of

L

is half as that of the same line, then the slope of

L

is :

Options

A $-3$
B $-3 / 8$
C $-3 / 2$
D $-3 / 16$

Correct answer

D. $-3 / 16$

Step-by-step solution

Given line

3 x+4 y=12

can be rewritten as

\begin{aligned}& \frac{3 x}{12}+\frac{4 y}{12}=1 \Rightarrow \frac{x}{4}+\frac{y}{3}=1 \\ & \Rightarrow x \text{-intercept }=4 \text{ and }y \text{-intercept }=3 \end{aligned}

Let

the required line be\mathrm{L}: \frac{x}{a}+\frac{y}{b}=1

where

a=x

-intercept and

b=y

-intercept According to the question

a=4 \times 2=8 and b=3 / 2\therefore

Required line is

\frac{x}{8}+\frac{2 y}{3}=1\Rightarrow 3 x+16 y=24\Rightarrow y=\frac{-3}{16} x+\frac{24}{16}

Hence, required slope =$\frac{-3}{16}.

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