Question

find the equation of the straight line parallel to 2x + 3y+11=0 and which is such that sum of intercspts on th axes is 15.

Answer 1

Given, a line l is parallel to a straight line  m whose equation is 2x+3y+11=0. 
Since the line l is parallel to the the line m, its equation will be 2x+3y+C=0.
In slope intercept form, the equation of the line l would be x/a + y/b = 1 ---- (2).
Given a+b=15 or a=15-b.
Therefore , the equation (2) can be written as 
x/(15-b) + y/b = 1
=>  bx + (15-b)y = (15-b)b
=>  bx + (15-b)y - (15-b)b = 0
Comparing the above with eq. (1), we get b = 2k, and (15-b)=3k for some factor k.
Solving for b, we get b = 6 and therefore a = 15-6 = 9. 
Thus, the equation of the line l is x/9 + y/6 =1 or 2x +3y -18 =0
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