What is the slope of a line parallel to this line 4x+5y=-3

First put it into slope intercept form. which is y=mx+b, in other words solve for y and get y by itself.

4x + 5y = - 3

5y = - 4x - 3

y = - 4/5x - 3/5

The slope of any line in slope intercept form is the m, or the coefficient to x.

In this line the slope will be - 4/5.

Now we find the slope of a line parallel to this line. Parallel lines have the same slope,

So the slope of a line parallel to 4x + 5y = - 3 is - 4/5

4x + 5y = - 3

5y = - 4x - 3

y = (-4/5) x - 3/5

Slopes of parallel lines are always the same.

The slope will be - 4/5.