To determine the constant of variation for the direct variation relationship [tex]\( y \)[/tex] and [tex]\( x \)[/tex], we start with the given information that [tex]\( y \)[/tex] varies directly as [tex]\( x \)[/tex]. This can be mathematically expressed as:
[tex]\[ y = kx \][/tex]
where [tex]\( k \)[/tex] is the constant of variation.
Given:
- [tex]\( y = 20 \)[/tex]
- [tex]\( x = 4 \)[/tex]
We substitute these values into the equation to solve for [tex]\( k \)[/tex]:
[tex]\[ 20 = k \cdot 4 \][/tex]
To isolate [tex]\( k \)[/tex], we divide both sides of the equation by 4:
[tex]\[ k = \frac{20}{4} \][/tex]
Simplifying the fraction:
[tex]\[ k = 5 \][/tex]
Therefore, the constant of variation [tex]\( k \)[/tex] for this relation is:
[tex]\[ \boxed{5} \][/tex]
