I don't think there is a special name for that. Note that not all functions can be described by a single equation - at least, not in a natural way. For example, a function may be described by parts.
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an algebraic equation that describes a relationship between several variables is called a?
A linear equation describes a line like 2x+1=y. If you were to graph that equation, then it would give you a line. A quadratic equation is like x^2+2x+1=y. Graphing this equation would give you a U shaped graph called a parabola.
A function is an equation (a relation) which has only one y-value for every x-value. If a single x-value has more than one y-value, the equation is no longer called a function.
A function describes a relation between several variables. For example the function f(x)=x2 describes a mapping from the variable x to a value that is the square of x. That is, for every real number we put as x, we will get a value for f(x). A function is defined for some domain and gets values from some range. An equation takes two terms and says they are equal. Usually both terms are functions of the same variable(s). For example, to build the equation x2 = x+2, we will use f(x) = x2, g(x) = x+2 and say that f(x)=g(x). Solving an equation means finding the set of values of the equation's variables which satisfy the equation. This set of values has to be part of the domains of the functions in both terms of the equation.
No a linear equation are not the same as a linear function. The linear function is written as Ax+By=C. The linear equation is f{x}=m+b.