Given: lines A 2x + 3y = 19 and B 2x + 3y + 7 = 0 also a line C 2x + 3y = 6.

To prove:

Line A and B are equidistant from the line C

Proof:

Let d1 be the distance between lines 2x + 3y = 19 and 2x + 3y = 6,

While d2 is the distance between lines 2x + 3y + 7 = 0 and 2x + 3y = 6

Hence proved, the lines 2x + 3y = 19 and 2x + 3y + 7 = 0 are equidistant from the line 2x + 3y = 6