Given information:
- The line is equally inclined to the axis.
- The length of the perpendicular from the origin upon the line is 2.

To find:
- A possible equation of the line.

Solution:
Let the line make an angle of θ with the positive x-axis. Then, it makes an angle of (90° - θ) with the positive y-axis.

Length of perpendicular from the origin upon the line = 2
This implies that the distance between the origin and the line is 2.

Using trigonometry, we can write:
tan θ = 2
tan (90° - θ) = 2

Solving these equations, we get:
θ = 63.43°
or
θ = 26.57°

Note: Both angles have the same tangent value of 2, so the line can make an angle of either θ or (90° - θ) with the x-axis.

Using the slope-intercept form of the equation of a line:
y = mx + c
where m is the slope and c is the y-intercept,

For θ = 63.43°:
m = tan θ = 2
c = 0 (since the line passes through the origin)
So, the equation of the line is:
y = 2x

For θ = 26.57°:
m = tan θ = 0.5
c = 0 (since the line passes through the origin)
So, the equation of the line is:
y = 0.5x

However, we need to check which of these equations satisfy the condition that the line is equally inclined to the axis.

For a line to be equally inclined to the axis, it must make equal angles with the x-axis and the y-axis. This implies that the slope of the line must be either 1 or -1.

Checking the slopes of the two lines we obtained:
For y = 2x, the slope is 2 which is not equal to 1 or -1.
For y = 0.5x, the slope is 0.5 which is not equal to 1 or -1.

Hence, neither of these lines satisfy the condition that the line is equally inclined to the axis.

Let's try another angle value for θ.

For θ = 116.57°:
m = tan θ = -2
c = 0 (since the line passes through the origin)
So, the equation of the line is:
y = -2x

Checking the slope of this line:
For y = -2x, the slope is -2 which is equal to -1/1.

Thus, the equation of the line that satisfies both the given conditions is:
x + y = 2

Therefore, option 'C' is the correct answer.