Which mathematical operation is used to calculate the constant of variation in direct variation problems?

Which mathematical operation is used to calculate the constant of variation in direct variation problems?

• A. Addition
• B. Subtraction
• C. Division
• D. Multiplication

Answer: (C)

In direct variation problems, the relationship between two variables can be expressed in the form \( y = kx \), where \( k \) is the constant of variation. To determine \( k \) when given specific values of \( y \) and \( x \), the mathematical operation applied is division. When you isolate \( k \), you rearrange the equation to \( k = \frac{y}{x} \). This shows that the constant of variation is found by dividing the value of \( y \) by the corresponding value of \( x \). The operation of division allows us to quantify how many times \( x \) fits into \( y \), ultimately providing us with the constant that describes the proportional relationship between the two variables. Thus, division is the key operation for calculating the constant of variation in direct variation scenarios.

In direct variation problems, the relationship between two variables can be expressed in the form ( y = kx ), where ( k ) is the constant of variation. To determine ( k ) when given specific values of ( y ) and ( x ), the mathematical operation applied is division.

When you isolate ( k ), you rearrange the equation to ( k = \frac{y}{x} ). This shows that the constant of variation is found by dividing the value of ( y ) by the corresponding value of ( x ). The operation of division allows us to quantify how many times ( x ) fits into ( y ), ultimately providing us with the constant that describes the proportional relationship between the two variables.

Thus, division is the key operation for calculating the constant of variation in direct variation scenarios.