Find the equation of a straight line that is parallel to 4y-3x+10=0

First, put the equation in slope intercept form: y=mx+b

4y-3x+10=0
Subtract 4y from both sides: (the zero cancels out because it's nothing)

-3x +10=-4y
Divide both sides by -4 to get y alone:

3/4x+5/2=y or  y=3/4x+5/2  (they are the same thing flipped either way). 

Now you have y=3/4x+5/2

To find a parallel line, you have to know that ALL parallel lines will have the same slope as the first line.

so the slope will be 3/4x

For the y intercept, you can choose any number you want OTHER than the one that was on the previous line. For example, you can have any of these equations to make it parallel to the first line:

y=3/4x+3
y=3/4x-6.55552
y=3/4x+10000259
y=3/4x-67487987.009999

Literally, the y intercept could be anything but 5/2