Question

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

Answer 1

Let us consider the equation to be of the form (x/a) + (y/a) = 1, since the x and the y-intercepts are equal. Now since this line passes through the point (2,3), this point should satisfy the equation considered, therefore substituting we have (2/a) + (3/a) = 1, therefore a=5. Thus, the equation is x+y=5.

Answer 2

$\mathtt{ \huge \fbox{SOLUTION :</p><p>}}$

Given ,

The x intercept (b) is equal to y intercept (a) i.e b = a

We know that , the intercept form is given by

$\mathtt{ \large \underline{ \fbox{ \frac{x}{a} + \frac{y}{b} = 1 }}}$

So ,

$\sf \hookrightarrow \frac{x}{a} + \frac{y}{a} = 1 \\ \\ \sf \hookrightarrow x + y = a - - - - (i)$

Since , the given line passes through the point (2,3) , so ,

$\sf \hookrightarrow 2 + 3 = a \\ \\ \sf \hookrightarrow a = 5$

On substituting the value of a = 5 in equation (i) , we obtain

x + y = 5 , which is the required equation of the line