The line passes through the point (1,2) and has an intercept sum of 20. This means a+b=20, where a and b are the x- and y-intercepts. The equation is set up as x/a + y/b = 1. Solving for a and b, the two possible equations are found to be x/19 + y/1 = 1 or x - 21y = 21.

1. Determine the equation of the line who's sum of it's intercepts on the axes is 20 and it passes
through the point (1,2).
Solution
We can write the equation of line in the form:
x/a+y/b = 1, where a and b are x and y intercepts of the line.
Given a+b = 20. Therefore we write b = 20-a, and rewrite the equation:
x/a+y/(2-a) = 1. Since this line passes through (1.2), it should satisfy a/a+y/(20-a) = 1. So
substitute x = 1, 1nd y = 2 in this equation and solve for a.
1/a+2/(20-a) = 1. Multiply by a(20-a)
20-a+2a = (20-a)a
20+a = 20a -a^2
20+a-20a+a^2 = 0
a^2-19a+20 = 0
(a-20)(a+1) = 0
a- 19 = 0 Or a+1 = 0.
If a= 19, then b = 20-19 = 1,
If a = -1, then b = 20- -1 = 21.
Therefore the equation of the lines are:
x/19 +y/1 = 1 Or x+19y = 19.....(1)
Also x/21+y/(-1) = 1 or -x+21y = -21 or
x-21y = 21..........(2)
(1) and (2) are the lines required