Coordinates

just out of curiosity, are you the same person that posted this a few weeks ago? Because I don't think that one ever got answered...

x/ a  + y/b = 1

Multiply both sides by ab

xb   +  ya   =  ab

Since this passes through   (1,11)  and ( 4,8)  we have this system

  1b +11a  = ab     ⇒  -4b -44a  = -4ab   (1)

  4b  + 8a   =  ab            (2)

Add (1)  and (2)

-36a   =  -3ab          since a  cannot =  0  ......divide by a

-36  = -3b

-36/ -3  =  b  = 12

Using (2)

4(12)  +  8a  =  a (12)

48  +  8a  =  12a

48  = 12a - 8a   

48 = 4a

48/4 = a  = 12

16/4 = a  =  4