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).

We'll write the intercept form of the equation of the
line:

x/a + y/b = 1,

where a
is x intercept and b is y intercept.

The sum of intercepts
on the axis is 20.

a+b = 20 => b = 20 -
a

We'll re-write the
equation:

x/a + y/(20 - a) =
1

We know that the line passes through the point
(1,2).

We'll substitute the coordinates of the point into
the equation of the line:

1/a + 2/(20-a) =
1

We'll calculate LCD:

(20-a)
+ 2a = a(20-a)

We'll remove the
brackets:

20 - a + 2a = 20a -
a^2

We'll move all terms to one
side:

20 + a - 20a + a^2 =
0

a^2 - 19a + 20 = 0

We'll
apply the quadratic formula:

a1 =
[19+sqrt(281)]/2

a2 =
[19-sqrt(281)]/2

We'll write the equations for both values
of a:

For a = [19+sqrt(281)]/2
=>

2x/[19+sqrt(281)] + 2y/[40 - 19 -sqrt(281)] =
1

2x/[19+sqrt(281)] + 2y/[21 -sqrt(281)] =
1

For [19-sqrt(281)]/2
=>  

2x/[19-sqrt(281)] + 2y/[40 - 19 +sqrt(281)] =
1

2x/[19-sqrt(281)] + 2y/[21+sqrt(281)] =
1