The equation of the line passing through (1,11) and \((4,8)\) can be expressed in the form
x/a + y/b = 1.
Find a.
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