According to the meaning of the question, these two straight lines are parallel to each other.

The straight line 2x-3y+6=0 means y=2/3x +2.

The straight line 2x-3y-7=0, that is, y=2/3x -7/3.

Take the point p (0,2) on the straight line y=2/3x+2, and according to the formula of point-line distance:

Distance d=l0×2-3×2-7l/√(2? +3? )

= 13/√ 13

=√ 13

Therefore, the given linear spacing is √ 13.

comment

The distance between lines exists only between parallel lines. Therefore, the distance between two parallel lines is required, and a special point can be taken on either line.

Then, the distance from this point to another straight line is calculated according to the formula of point-line distance, that is, the distance between lines is obtained from the point-line distance.

This embodies the transformation idea in mathematics and can transform the topic well.