To solve the problem where [tex]\( y \)[/tex] varies directly with [tex]\( x \)[/tex], we need to use the concept of direct variation, which means [tex]\( y = kx \)[/tex] for some constant [tex]\( k \)[/tex].
1. Determine the constant [tex]\( k \)[/tex]:
- We are given that [tex]\( y = 14 \)[/tex] when [tex]\( x = -4 \)[/tex].
- Substitute these values into the equation to find [tex]\( k \)[/tex]:
[tex]\[
14 = k \times (-4)
\][/tex]
- Solve for [tex]\( k \)[/tex]:
[tex]\[
k = \frac{14}{-4} = -3.5
\][/tex]
2. Use the constant [tex]\( k \)[/tex] to find the new value of [tex]\( y \)[/tex] when [tex]\( x = -6 \)[/tex]:
- Substitute [tex]\( k \)[/tex] and the new [tex]\( x \)[/tex] value into the direct variation equation:
[tex]\[
y = k \times (-6)
\][/tex]
- Substitute [tex]\( k = -3.5 \)[/tex]:
[tex]\[
y = -3.5 \times (-6) = 21
\][/tex]
Thus, the value of [tex]\( y \)[/tex] when [tex]\( x = -6 \)[/tex] is [tex]\( 21 \)[/tex].
Therefore, the correct answer is
[tex]\[ \boxed{21} \][/tex]
