Given:

9x + 6y – 7 = 0 and 3x + 2y + 6 = 0 are parallel lines

To find:

The equation of the line mid-way between the givens line

Explanation:

The given equations of the lines can be written as:

… (1)

3x + 2y + 6 = 0 … (2)

Let the equation of the line midway between the parallel lines (1) and (2) be

3x + 2y + λ = 0 … (3)

The distance between (1) and (3) and the distance between (2) and (3) are equal.

Equation of the required line:

⇒ 18x + 12y + 11 = 0

Hence, equation of required line is 18x + 12y + 11 = 0.