When solving for a variable, the ultimate goal is to get the desired variable on one side of the equal sign and everything else on the other side. In order to do this, you need to do what's called the
"inverse operation" of everything next do the desired variable (for multiplication,...

By "golden rule" you may be thinking of the Fundamental Theorem of Calculus, which states that the derivative of the integral of a function is just equal to the original function (they cancel out). On the other hand, the integral of the derivative of a function is equal to the value of...

The slope-intercept form is a way of describing a line that is designed to make two pieces of information immediately available: the slope (m), and the y-intercept (b). You will need these to pieces of information to put the line in slope-intercept form: y=mx + b
The y-intercept (b) is already...