The equation of a line in the intercept form is xa+yb=1 ..(i)
where a and b are the intercepts on x and y axis respectively.
It is given that the line cuts off equal intercepts on both the axes. This means that a=b.
Accordingly, equation(i) reduces to,
xa+yb=1 ⇒x+y=a ...(ii)
Since the given line passes through point (2,3), equation(ii) reduces to 2+3=a⇒a=5
On substituting the value of a in equation (ii), we obtain
x+y=5 which is the required equation of the line.