Identifying direct variation equations If it does, find the constant of variation and write it in simplest form. \( 5 y=20 x \) Direct variation \( 2 x+7 y=-9 \) Not direct variation Direct variation Not direct variation

To determine if an equation represents a direct variation, you can rearrange it into the form \( y = kx \), where \( k \) is the constant of variation. For the equation \( 5y = 20x \), divide both sides by 5 to get \( y = 4x \). Here, the constant of variation \( k \) is 4, which means it is a direct variation! On the flip side, for the equation \( 2x + 7y = -9 \), you can see that it cannot be rewritten clearly as \( y = kx \) because it involves both \( x \) and \( y \) in a way that mixes them up. Therefore, this one is indeed not direct variation!