For each equation, determine whether it shows a direct variation (that is, shows directly proportional variables). If it does, find the constant of variation and write it in simplest form. \( \begin{array}{l}3 x=-6 y-1 \\ 10 y=5 x \\ \text { Not direct variation variation } \\ \text { Direct variation }\end{array} \)

To determine if the equations show direct variation, we look for the form \( y = kx \), where \( k \) is the constant of variation. For the first equation, \( 3x = -6y - 1 \), we can rearrange it to isolate \( y \): \[ 6y = -3x - 1 \implies y = -\frac{1}{2}x - \frac{1}{6} \] Since there is a constant term \(-\frac{1}{6}\), this does not show direct variation. For the second equation, \( 10y = 5x \), rearranging gives: \[ y = \frac{5}{10}x = \frac{1}{2}x \] This shows direct variation with a constant of variation \( k = \frac{1}{2} \). So, the answer is: 1. Not direct variation 2. Direct variation with \( k = \frac{1}{2} \)