find the equation to the straight line passing through the point(3,-4) and cutting off intercepts, equal but of opposite signs, from the two axes

Let the coordinates are A: (a,0) and B:(0,-a) ,and the point P:(3,-1)is on the line therefore , slope of AP=slope of BP. ( -4 -0)÷(3-a) = (-4+a)÷(3-0)By solving this ,we get the value of a= 7Now the coordinates are (7,0) and (0,-7) Therefore ,by two point form of line We get ,(Y-0)=(-7 -0)÷(0-7)×(x-7)X-Y-7=O, is the required equation.