# find the equation of a straight line passes through a point (2,3) which makes x-intercept double the y-intercept.

Solution)

Let the equation makes an intercept of 'a' with axis.

Therefore, intercept on x - axis = 2a.

The equation of the line is given by

$\frac{x}{2a}+\frac{y}{a}=1\phantom{\rule{0ex}{0ex}}x+2y=2a...\left(i\right)$

This equation passes through the point (2,3).

So, from (i), we have,

2+2(3)=2a

2+6=2a

8=2a

a = 4

Thus, the required equation of the line is

$x+2y=2a\phantom{\rule{0ex}{0ex}}x+2y=2\left(4\right)\{putthevalueofa\}\phantom{\rule{0ex}{0ex}}x+2y=8\phantom{\rule{0ex}{0ex}}Regards!\phantom{\rule{0ex}{0ex}}$

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