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Simple question:

Why do refer to the equation of a straight line instead of the formula of a straight line?

For instance, formulae provide relationships between multiple variables, which is what something like $y=mx+c$ does. Equations, on the other hand, assert equality (which admittedly $y=mx+c$ does) but we tend to want them solved.

PhysicsMathsLove
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  • @Somos What I am trying to ask is why everyone talks about equations of graphs rather than formulae of graphs. It is common to describe $y=2x+1$ as an equation for the graph, but I am wondering why it is not as common to refer to it as a formula for the graph. – PhysicsMathsLove Mar 21 '21 at 12:22

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One good reason to prefer the equation of a geometric object is if you go beyond one linear equation in one variable. For example, an equation of a circle is $\,(x-a)^2+(y-b)^2=r^2.\,$ Here, both variables $\,x\,$ and $\,y\,$ are treated simultaneously. If written as a formula $\,y = \text{[something]}\,$ then there are two values of $\,y\,$ for values of $\,x.\,$ A similar example is the equation of a degenerate conic being two lines. The equation is something like $\, 0 = (y-ax-b)(y-cx-d).\,$ Again, writing $\,y\,$ as a formula needs two values.

Somos
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