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What is the equation of the straight line passing through the point $(2,3)$ and making an intercept on the positive y-axis equal to twice its intercept on the positive x-axis?
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Verified Answer
The correct answer is:
$2 x+y=7$
Given line passes through $(2,3)$
Intercept form: $\frac{x}{a}+\frac{y}{b}=1$
$\Rightarrow \frac{x}{a}+\frac{y}{2 a}=1$
$\Rightarrow 2 \mathrm{x}+\mathrm{y}=2 \mathrm{a}$
But this passes through $(2,3)$ $\therefore 2 \mathrm{a}=2(2)+3=7$
$\Rightarrow a=\frac{7}{2}$
$\therefore$ Equation of line is $2 \mathrm{x}+\mathrm{y}=2\left(\frac{7}{2}\right)$
$\Rightarrow 2 x+y=7$
Intercept form: $\frac{x}{a}+\frac{y}{b}=1$
$\Rightarrow \frac{x}{a}+\frac{y}{2 a}=1$
$\Rightarrow 2 \mathrm{x}+\mathrm{y}=2 \mathrm{a}$
But this passes through $(2,3)$ $\therefore 2 \mathrm{a}=2(2)+3=7$
$\Rightarrow a=\frac{7}{2}$
$\therefore$ Equation of line is $2 \mathrm{x}+\mathrm{y}=2\left(\frac{7}{2}\right)$
$\Rightarrow 2 x+y=7$
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