equation of line which passes through (x,y) and sum of whose coordinate axis is A

Question

equation af line which contains ,the point A(2,2) and sum of whose intercepts ison coordinate axis is 9

 

Answer 1

Let the equation of the line be y=mx+b.

The y-intercept is b and the x-intercept is -b/m, so b-b/m=9 therefore m=b/(b-9).

Also, plugging in (2,2): 2=2m+b=2b/(b-9)+b by substituting for m.

Multiply through by b-9: 2(b-9)=2b+b(b-9).

So 2b-18=2b+b²-9b, b²-9b+18=0=(b-6)(b-3). So we have two possible values for b=3, 6 and the corresponding values of m are 3/(3-9)=-1/2 and 6/(6-9)=-2.

So there are two lines fulfilling the given conditions:

y=-x/2+3 (y-int = 3, x-int = 6) and y=-2x+6 (y-int = 6, x-int = 3), so sum of intercepts is 9. And both lines pass through A(2,2), which is where the two lines intersect each other.