To solve for [tex]\( k \)[/tex], the constant of variation, in a direct variation problem, we start with the equation that describes direct variation:
[tex]\[ y = k \cdot x \][/tex]
Here, [tex]\( y = 240 \)[/tex] and [tex]\( x = 30 \)[/tex]. We need to find the value of [tex]\( k \)[/tex].
1. Substitute the given values for [tex]\( y \)[/tex] and [tex]\( x \)[/tex] into the direct variation equation:
[tex]\[ 240 = k \cdot 30 \][/tex]
2. To isolate [tex]\( k \)[/tex], divide both sides of the equation by [tex]\( 30 \)[/tex]:
[tex]\[ k = \frac{240}{30} \][/tex]
3. Simplify the fraction:
[tex]\[ k = 8 \][/tex]
Thus, the constant of variation [tex]\( k \)[/tex] is [tex]\( \boxed{8} \)[/tex].
