Question

How do you find the slope of a line perpendicular to `3x+10y=-20`?

Answer 1

Consider your line written in a friendlier form as:
`y=-3/10x-2` (I isolated `y` on one side)
here you can "read" the slope `m` of your line which is `m=-3/10` (the coefficient of `x`);
Now, the line perpendicular will have slope `m_1=-1/m`
or: `m_1=10/3`