Question 9 1 pts Tell whether the following equation represents a direct variation. If so, identify the constant of variation. \[ 12 y=3 x \] Yes; \( k=\frac{1}{4} \) Yes: \( k=3 \) Yes; \( k=4 \) No

To determine if the equation \( 12y = 3x \) represents a direct variation, we can rewrite it in the standard form \( y = kx \). By isolating \( y \), we see that \( y = \frac{3}{12}x = \frac{1}{4}x \). Since this can be expressed as \( y = kx \), where \( k = \frac{1}{4} \), it clearly demonstrates direct variation. In direct variation, if you double the value of \( x \), \( y \) also doubles. It’s like measuring how fast you can fill a bowl with water; if you pour in water at a constant rate, the amount increases directly with the time you pour. This consistent ratio is what direct variation is all about!