An equation that defines y as a function of x is given. (a) Solve for y in terms of x and replac

step 1 Given equation is x plus 3y equals to 12 in this question we have to solve for y in terms of x a

An equation that defines y as a function of x is given. (a)...

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Key Concepts

Linear Equations

A linear equation is an algebraic expression that shows a straight-line relationship between variables. In this context, the equation involves variables x and y linked by constants, and the task is to express one variable in terms of the other, enabling further analysis or graphical representation.

Isolating a Variable

Isolating a variable involves algebraically rearranging an equation so that one variable stands alone on one side of the equation. This technique is used to rewrite the equation in a form that makes it easy to interpret or apply specific operations like substitution.

Function Notation

Function notation is a way to represent a relationship between inputs and outputs by writing the output as a function of the input, typically using f(x). This notation provides a clear framework for understanding and manipulating equations that model functions.

Function Evaluation

Function evaluation involves substituting a specific value into a function to compute the corresponding output. Once the function is defined in terms of f(x), evaluating it at any given input involves replacing the variable with the specific number to get the result.

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