Will help you prepare for the material covered in the next...

Will help you prepare for the material covered in the next section.
a. If $y=\frac{k}{x}$, find the value of $k$ using $x=8$ and $y=12$.
b. Substitute the value for $k$ into $y=\frac{k}{x}$ and write the resulting equation.
c. Use the equation from part (b) to find $y$ when $x=3$.

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Key Concepts

Inverse Variation

Inverse variation describes a relationship between two variables in which their product is constant; as one variable increases, the other decreases proportionally. This concept is fundamental in understanding how changes in one quantity affect another when the relation is given by an inverse proportionality.

Constant of Variation

The constant of variation (or constant of proportionality) is the fixed value that results from multiplying the two variables in an inverse variation. Determining this constant is crucial because it encapsulates the specific relationship between the variables and allows for the prediction of one variable given the other.

Algebraic Substitution

Algebraic substitution involves replacing a variable with a known value or expression to simplify or solve an equation. This method is essential in applying known data to a general formula in order to find unknown quantities within that equation.

Solving Rational Equations

Rational equations are equations that include fractions with variables in the denominators. Solving these equations typically involves techniques such as eliminating the fractions by multiplying through by a common denominator and then isolating the variable of interest to find its value.

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