General Certificate of Secondary Education (GCSE) Maths Practice Exam

When a variable \( y \) is said to be inversely proportional to another variable \( x \), it means that as \( x \) increases, \( y \) decreases in such a way that their product remains constant. This relationship can be expressed mathematically as \( y = \frac{k}{x} \), where \( k \) is a constant.

In this equation, if \( x \) takes on larger values, \( y \) must take on smaller values to ensure that the product \( y \times x \) equals the constant \( k \). Conversely, if \( x \) is smaller, \( y \) will be larger, maintaining that constant product. Thus, the equation \( y = \frac{k}{x} \) precisely captures the essence of inverse proportionality between \( y \) and \( x \).

The other forms provided in the choices do not accurately represent inverse relationships. For instance, the equation \( y = k + x \) suggests a direct addition rather than an inverse association, while \( y = kx \) indicates direct proportionality. The equation \( y = \frac{x}{k} \) would imply that \( y \) is directly proportional to \( x \)