Certainly! Let's solve for [tex]\( k \)[/tex] step by step.
1. Understand the relationship: The problem states that [tex]\( y \)[/tex] varies directly with [tex]\( x \)[/tex]. This means we can use the direct variation formula:
[tex]\[ y = kx \][/tex]
2. Substitute the given values: We're given that [tex]\( y = -16 \)[/tex] and [tex]\( x = 4 \)[/tex]. Plug these values into the equation:
[tex]\[ -16 = k \times 4 \][/tex]
3. Solve for [tex]\( k \)[/tex]: Isolate [tex]\( k \)[/tex] by dividing both sides of the equation by 4:
[tex]\[ k = \frac{-16}{4} \][/tex]
4. Simplify the result:
[tex]\[ k = -4 \][/tex]
So, the constant of variation [tex]\( k \)[/tex] is [tex]\(-4\)[/tex].
Therefore,
[tex]\[ k = -4.0 \][/tex]
