In a direct variation, the relationship between \( x \) and \( y \) can be expressed as:
\[ y = kx \]
where \( k \) is a constant.
We know that when \( x = 2 \), \( y = 24 \). We can use this information to find \( k \):
\[ 24 = k(2) \]
To find \( k \), divide both sides by 2:
\[ k = \frac{24}{2} = 12 \]
Now that we have \( k \), we can write the equation of direct variation:
\[ y = 12x \]
Now we want to find \( y \) when \( x = 7 \):
\[ y = 12(7) = 84 \]
Thus, when \( x = 7 \), \( y = 84 \).