Question 254976
There is the standard form and the slope intercept form.

y=mx+b is the slope intercept form
where m is the slope and b is the y intercept when x=0

The standard form is ax+by=c
where the slope is -a/b
The b's mean different things in each equation. Don't get confused. They are not the same b.
Let's look at your equation 2x-3y=-6
It is in standard form
The slope is -a/b=-(2/-3)=2/3
We want a line parallel which means with the same slope.
(y-y1)=2/3(x-x1)
y-(-3)=2/3(x-(-5))
y+3=2/3(x+5)
y+3=2/3x+2/3(5)
y+3=2x/3+10/3
Subtract 3 from both sides
10/3=3 1/3
y=2x/3+1/3 in slope intercept form
Multiply by 3
3y=2x+1
Subtract 2x
-2x+3y=1 in standard form