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  • If the x- intercept of some line L is double as that of the line, 3x+4y=12 and the y- intercept of L is half as that of the same line, then the slope of L is:Opt

If the x- intercept of some line L is double as that of the line, 3x+4y=12 and the y- intercept of L is half as that of the same line, then the slope of L is:

Option: 1

-3


Option: 2

-\frac{3}{8}


Option: 3

-\frac{3}{2}


Option: 4

-\frac{3}{16}


Answers (1)

best_answer

\\\text{Given line } 3 x+4 y=12 \text{ can be rewrittel as}\\ \frac{3 x}{12}+\frac{4 y}{12}=1 \Rightarrow \frac{x}{4}+\frac{y}{3}=1\\ \Rightarrow x -intercept =4 \text{ and } \;y -intercept =3.\\\text{ Let the required line be} \\L: \frac{x}{a}+\frac{y}{b}=1\\ \text{ where } a=x -intercept\text{ and } b=y -intercept \\ \text{According to the question}

\\a=4 \times 2=8\text{ and }b=3 / 2\\ \text{ 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}

 

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