To find the constant of variation in the relation where [tex]\( y \)[/tex] varies directly as [tex]\( x \)[/tex], we use the direct variation formula:
[tex]\[ y = kx \][/tex]
Here, [tex]\( y \)[/tex] and [tex]\( x \)[/tex] are given as 20 and 4, respectively. We need to determine the constant [tex]\( k \)[/tex].
1. Start with the equation for direct variation:
[tex]\[ y = kx \][/tex]
2. Substitute the given values [tex]\( y = 20 \)[/tex] and [tex]\( x = 4 \)[/tex]:
[tex]\[ 20 = k \cdot 4 \][/tex]
3. Solve for [tex]\( k \)[/tex] by dividing both sides of the equation by 4:
[tex]\[ k = \frac{20}{4} \][/tex]
4. Simplify the right-hand side to find [tex]\( k \)[/tex]:
[tex]\[ k = 5 \][/tex]
Thus, the constant of variation [tex]\( k \)[/tex] is:
[tex]\[ \boxed{5} \][/tex]
