The equation of a line that forms a right-angled triangle with the axes can be determined by considering the given information: the area of the triangle and the length of its hypotenuse.

Given Information:
- Area of the triangle = 6 sq. units
- Hypotenuse length = 5 units

To find the equation of the line, we will follow these steps:

1. Find the length of the base and height of the triangle:
- The area of a triangle is given by the formula: Area = (1/2) * base * height
- We are given the area as 6 sq. units, so we can set up the equation: 6 = (1/2) * base * height

2. Use the Pythagorean theorem to find the lengths of the base and height:
- The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
- In this case, the hypotenuse length is given as 5 units, so we can set up the equation: 5^2 = base^2 + height^2

3. Solve the system of equations:
- We have two equations with two unknowns (base and height), so we can solve them simultaneously.
- Rearrange the first equation to express height in terms of the base: height = (12/base)
- Substitute this expression for height in the second equation: 5^2 = base^2 + (12/base)^2
- Simplify the equation: 25 = base^2 + 144/base^2
- Multiply through by base^2 to eliminate the fraction: 25base^2 = base^4 + 144
- Rearrange the equation to form a quadratic equation: base^4 - 25base^2 + 144 = 0

4. Solve the quadratic equation:
- We can solve the above equation by factoring or using the quadratic formula.
- After solving, we find two possible values for the base: base = ±3
- Substituting these values into the first equation, we can find the corresponding heights: height = ±4

5. Determine the equation of the line:
- The line that forms the triangle with the axes passes through the points (base, 0) and (0, height).
- Using the values of base and height, we find two possible equations:
- y = 4x/3 (for base = 3 and height = 4)
- y = -4x/3 (for base = -3 and height = -4)

Thus, the equation of the line that forms a right-angled triangle with the axes, with an area of 6 sq. units and a hypotenuse of 5 units, can be either y = 4x/3 or y = -4x/3.