Question 402265
OK step one: find slope of given function, which means put it in slope intercept form, so y=mx+b, so solve for y.
2x+3y=7 subtract 2x from each side
3y=-2x+7 divide both sides by 3
y=-2x/3+7/3  so slope for this line is m=-2/3
However, our line is perpendicular to this one, so the slope for OUR line is m=3/2 (opposite sign and flip it)
Now we use the point given and this slope and plug it into the point slope formula, which is 
y-y1=m(x-x1) where (x1,y1) is the given point so (-3,5)
{{{y-5=(3/2)(x+3)}}}
{{{y-5=3x/2+9/2}}} add 5 to each side
{{{y=3x/2+19/2}}} so this is your slope intercept form. 
For standard form just subtract 3x/2 from each side
{{{-3x/2+y=19/2}}}