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Question

(A) Let the $y$-intercept of the line be $a$. Then the $x$-intercept is $2a$. Using the intercept form of the line equation,$\frac{x}{2a} + \frac{y}{a

Vedclass · Accepted Answer

$x+2y-8=0$

Vedclass · Answer

(A) Let the $y$-intercept of the line be $a$. Then the $x$-intercept is $2a$. Using the intercept form of the line equation,$\frac{x}{2a} + \frac{y}{a} = 1$. Since the line passes through the point $(2,3)$,we substitute these coordinates into the equation: $\frac{2}{2a} + \frac{3}{a} = 1$ $\frac{1}{a} + \frac{3}{a} = 1$ $\frac{4}{a} = 1 \Rightarrow a = 4$. Substituting $a=4$ back into the intercept form: $\frac{x}{8} + \frac{y}{4} = 1$ Multiplying by $8$,we get $x + 2y = 8$,or $x + 2y - 8 = 0$. Thus,the correct option is $A$.

The equation of the line passing through the point $(2,3)$ such that its $x$-intercept is twice its $y$-intercept is ......... .

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