Question 748574
First, find the slope of 3x+2y=5.  
To do this, get it into slope-intercept form (y=mx+b where m is the slope and +b is the intercept.)

{{{3x+2y=5}}}

Subtract 3x from both sides:

{{{2y = -3x+5}}}

Divide both sides by 2:

{{{y = -3/2*x+5/2}}}

The coefficient of x is the slope in this equation, so the slope is:

{{{-3/2}}}

To find a perpendicular slope, you flip it over and change the sign, so it will go from:

{{{-3/2}}}

To:

{{{2/3}}}

So you want the line with slope 2/3 that has a y-intercept of 1 as required by the problem.

With slope-intercept form (y=mx+b), you just need to plug in your slope, m, which is 2/3 and your y-intercept, +b, which is positive 1:

{{{y=2/3*x+1}}}