To solve the problem where [tex]\( y \)[/tex] varies directly with [tex]\( x \)[/tex] and we need to find the constant of variation ([tex]\( k \)[/tex]), we start by using the relationship for direct variation:
[tex]\[ y = k \cdot x \][/tex]
Given:
- [tex]\( y = 30 \)[/tex]
- [tex]\( x = 6 \)[/tex]
Substitute these values into the direct variation equation:
[tex]\[ 30 = k \cdot 6 \][/tex]
To find [tex]\( k \)[/tex], isolate [tex]\( k \)[/tex] by dividing both sides of the equation by 6:
[tex]\[ k = \frac{30}{6} \][/tex]
Simplify the fraction:
[tex]\[ k = 5 \][/tex]
Therefore, the value of [tex]\( k \)[/tex] is 5.
