Question

Find the equation of the line that cuts off equal intercepts on the coordinate axes and passes through the point(4,7)

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.