What is the line that is parallel to 2x-3y=1 ? what is the slope of the line that is perpendicular to 2x-3y=1 ?

The equation of a line parallel to 2x - 3y = 1 will look exactly the same as this one, EXCEPT you'll have a different constant (i. e., a constant term not equal to 1).
                                                                        1 - 2x
Solve 2x - 3y = 1 for y:   -3y = 1 - 2x, or   y =
                                                                           -3

in which the slope, m, is 2/3.  The slope of a line perpendicular to 2x - 3y = 1 would be the negative reciprocal of 2/3; that is -3/2 (answer)