# 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).

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

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.

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