How do I find the slope of the line in simple form?

4x+5y=3

use a two step process

1. take all terms except the y term to the right side

4x + 5y = 3 ----> 5y = -4x + 3

2. divide each term by the coefficient of the y term
5y = -4x + 3
y = (-4/5)x + 3/5

now you have it in the form y = mx + b, where m is the slope, so

the slope is -4/5