Question 1052371
Parallel to 2x+3y=5, will have the same slope, which if solve for y in terms of x and look at coefficient on x, is {{{-2/3}}}.   Such line to pass through the given point, using point-slope form, is {{{y-1=-(2/3)(x+2)}}}.



Perpendicular to 2x-3y=5, will have a slope negative reciprocal of that for this given line.  Solve this given equation for y in terms of x, take the negative reciprocal of coefficient on x, and it will be  {{{-3/2}}}.  The line passing through the given point with this slope is, in point-slope form,  {{{y-1=-(3/2)(x+2)}}}.



<a href="https://www.youtube.com/watch?v=DSGJJekmXjQ">converting between point-slope and slope-intercept forms</a>


That should help you see how to also understand the standard form Ax+By=C.   You CAN find the slope if you learn how to read this form of equation.


The work I described and did, could be done all in standard form, if you learn to read and use the standard form equation.