Given: equation parallel to 3x – 4y + 6 = 0 and passing through the middle point of the join of points (2, 3) and (4, -1). 

To find: 

The equation to the straight line parallel to 3x – 4y + 6 = 0 and passing through the middle point of the join of points (2, 3) and (4, -1). 

Explanation: 

Let the Given points be A (2, 3) and B (4, − 1). Let M be the midpoint of AB. 

∴ Coordinates of M = \(\Big(\frac{2+4}{2},\frac{3-1}{2}\Big)\) = (3,1)

The equation of the line parallel to 3x − 4y + 6 = 0 is 3x – 4y + λ = 0 

This line passes through M (3, 1). 

∴ 9 – 4 + λ = 0 

⇒ λ = -5 

Substituting the value of λ in 3x – 4y + λ = 0, we get 3x – 4y – 5 = 0 

Hence, the equation of the required line is 3x – 4y – 5 = 0.