21. Which of the following equations is not an example of a direct variation equation? (Circle your answer) \( \begin{array}{llll}\text { a. } y=x & \text { b. } y=\frac{1}{4} x & \text { c. } y=5 x-2 & \text { d. } y=9 x\end{array} \)

A **direct variation** equation is one that can be written in the form \( y = kx \), where \( k \) is a constant of proportionality. In such equations, \( y \) varies directly as \( x \), meaning that as \( x \) increases or decreases, \( y \) does so proportionally without any additional terms. Let's analyze each option: - **a. \( y = x \)** This fits the form \( y = kx \) with \( k = 1 \). **Direct variation.** - **b. \( y = \frac{1}{4}x \)** This also fits the form \( y = kx \) with \( k = \frac{1}{4} \). **Direct variation.** - **c. \( y = 5x - 2 \)** This equation includes an additional constant term (\(-2\)) and cannot be written purely in the form \( y = kx \). **Not a direct variation.** - **d. \( y = 9x \)** This fits the form \( y = kx \) with \( k = 9 \). **Direct variation.** **Answer:** **c. \( y = 5x - 2 \)**