find the equation of the line which is parallel to the line 2x-3y=5 and is such that sum of its intercepts on the axes is 6

Question

find the equation of the line which is parallel to the line 2x-3y=5
and is such that sum of its intercepts on the axes is 6

Anuradha Sharma · Accepted Answer

Sum of intercept on the axes is 6 so let  x -axis intercept = aso y -axis intercept = 6-aNow equation of line will be,xa+yb=1xa+y6-a=1x6-a+ay=a6-aSlop of this line is same as that of 2x-3y=5So -6+aa=23-18+3a=2aa = 18So equation of line is x6-18+18y=18×-12-2x+3y=-362x-3y=36