What is the formula for direct variation where y varies directly as x^n?

What is the formula for direct variation where y varies directly as x^n?

• A. y = k/x
• B. y = kx
• C. y = kx^n
• D. y = kn^x

Answer: (C)

In the context of direct variation, when it is stated that \( y \) varies directly as \( x^n \), it means that there is a constant \( k \) such that the relationship can be expressed as \( y = kx^n \). Here, \( k \) is a non-zero constant that represents the ratio of \( y \) to \( x^n \) for any point in the relationship. The term "varies directly" signifies that as \( x^n \) increases, \( y \) increases proportionally, and vice versa. The exponent \( n \) indicates that the relationship involves a power of \( x \), making it distinctly different from more straightforward linear relationships, which would involve just \( x \) without an exponent. For instance, if \( k \) is determined to be 2 and \( n \) is 3, then the equation becomes \( y = 2x^3 \). This indicates that doubling \( x^3 \) would result in doubling \( y \), illustrating the nature of direct variation. Other options do not represent the concept of direct variation with respect to a power of \( x \): - The formula involving \( k/x \) depicts an

In the context of direct variation, when it is stated that ( y ) varies directly as ( x^n ), it means that there is a constant ( k ) such that the relationship can be expressed as ( y = kx^n ). Here, ( k ) is a non-zero constant that represents the ratio of ( y ) to ( x^n ) for any point in the relationship.

The term "varies directly" signifies that as ( x^n ) increases, ( y ) increases proportionally, and vice versa. The exponent ( n ) indicates that the relationship involves a power of ( x ), making it distinctly different from more straightforward linear relationships, which would involve just ( x ) without an exponent.

For instance, if ( k ) is determined to be 2 and ( n ) is 3, then the equation becomes ( y = 2x^3 ). This indicates that doubling ( x^3 ) would result in doubling ( y ), illustrating the nature of direct variation.

Other options do not represent the concept of direct variation with respect to a power of ( x ):

• The formula involving ( k/x ) depicts an