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Question

(A) The equation of a line in the intercept form is $\frac{x}{a} + \frac{y}{b} = 1$ $(i)$.Given that the line cuts off equal intercepts on both axes,w

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$x + y = 5$

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(A) The equation of a line in the intercept form is $\frac{x}{a} + \frac{y}{b} = 1$ $(i)$.Given that the line cuts off equal intercepts on both axes,we have $a = b$.Substituting $b = a$ in $(i)$,we get $\frac{x}{a} + \frac{y}{a} = 1$,which simplifies to $x + y = a$ $(ii)$.Since the line passes through the point $(2, 3)$,we substitute these coordinates into $(ii)$:$2 + 3 = a \Rightarrow a = 5$.Substituting $a = 5$ back into $(ii)$,the required equation of the line is $x + y = 5$.

Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point $(2,3)$.

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