which equation is equivalent to

An equation is any expression with an equals sign, so your example is by definition an equation. Equations appear frequently in mathematics because mathematicians love to use equal signs. A formula is a set of instructions for creating a desired result. Non-mathematical examples include such things as chemical formulas (two H and one O make H2O), or the formula for Coca-Cola (which is just a ... The confusion here seems to be about how translation and other transformations apply to the equation of a circle, which is not a function in the sense of passing the vertical line test but rather an implicit relation. Let's clear up the confusion: Translation: For the circle's equation $ (x - x_1)^2 + (y - y_1)^2 = r^2 $, the $ x_1 $ and $ y_1 $ terms represent the coordinates of the center of ... YouTube on MSN: What are equivalent equations - why we have to use properties of equality What are equivalent equations - why we have to use properties of equality It seems to me an equation, in an abstract sense, must always involve some varying quantities where the varying quantities belong in some space (set, algebraic structure, what have you). In order to

If we want an equation $f (x, y)$ for the line, the domain of $f$ can only be the shadow of the line on the $xy$ plane. But any nice function $f$ will have as a domain either all pairs $ (x, y)$, or almost all of them. What is the equation for a 3D line? - Mathematics Stack Exchange