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

Dear Student,
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 
$$\begin{gathered} \frac{x}{2a}+\frac{y}{a}=1 \\ x+2y=2a...\left(i\right) \end{gathered}$$
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
$$\begin{gathered} x+2y=2a \\ x+2y=2\left(4\right) \{put the value of a\} \\ x+2y=8 \\ Regards! \end{gathered}$$

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