Given: equations are as follows:

y = √3 x + 1……(1)

y = 4 …….(2)

y = - √3 x + 2…….(3)

Assuming:

In triangle ABC, let equations (1), (2) and (3) represent the sides AB, BC and CA, respectively.

To prove:

Lines y = √3 x + 1, y = 4 and y = - √3 x + 2 form an equilateral triangle.

Explanation:

Solving (1) and (2):

x = √3 , y = 4

Thus, AB and BC intersect at B(√3,4)

Solving (1) and (3):

Thus, AB and CA intersect at A(,)

Similarly, solving (2) and (3):

, y = 4

Thus, BC and AC intersect at C(,4)

Now, we have:

Hence Proved, the given lines form an equilateral triangle