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

The equation that is not an example of a direct variation equation is \( y = 5x - 2 \). Direct variation equations have the form \( y = kx \), where \( k \) is a non-zero constant. This means that when \( x = 0 \), \( y \) must also equal 0. However, in \( y = 5x - 2 \), when \( x = 0 \), \( y \) equals \(-2\), which clearly shows that it doesn't pass through the origin. To identify direct variation, look for equations that can be expressed purely as \( y = kx \). If there's any constant added or subtracted (like \(-2\) in option c), it’s a sign that the equation represents a different relationship, indicating that it is not a direct variation. Happy calculating!