Inverse variation, also known as inverse proportion, is a relationship between two variables where their product is constant. That means if [tex]\( x \)[/tex] and [tex]\( y \)[/tex] are in inverse variation, then [tex]\( x \cdot y = k \)[/tex] where [tex]\( k \)[/tex] is a constant.
Let's analyze each option to check if [tex]\( x \cdot y \)[/tex] is constant for the given pairs:
Option A:
[tex]\( x = [6, 4, 3, -2] \)[/tex]
[tex]\( y = [36, 24, 18, -12] \)[/tex]
- [tex]\( 6 \cdot 36 = 216 \)[/tex]
- [tex]\( 4 \cdot 24 = 96 \)[/tex]
- [tex]\( 3 \cdot 18 = 54 \)[/tex]
- [tex]\( -2 \cdot -12 = 24 \)[/tex]
The products are not constant.
Option C:
[tex]\( x = [2, 5, 8, 10] \)[/tex]
[tex]\( y = [5, 8, 11, 13] \)[/tex]
- [tex]\( 2 \cdot 5 = 10 \)[/tex]
- [tex]\( 5 \cdot 8 = 40 \)[/tex]
- [tex]\( 8 \cdot 11 = 88 \)[/tex]
- [tex]\( 10 \cdot 13 = 130 \)[/tex]
The products are not constant.
Option B:
[tex]\( x = [2, 3, 4, -6] \)[/tex]
[tex]\( y = [18, 12, 9, -6] \)[/tex]
- [tex]\( 2 \cdot 18 = 36 \)[/tex]
- [tex]\( 3 \cdot 12 = 36 \)[/tex]
- [tex]\( 4 \cdot 9 = 36 \)[/tex]
- [tex]\( -6 \cdot -6 = 36 \)[/tex]
The products are constant and equal to 36.
Option D:
[tex]\( x = [-6, -4, 5, 15] \)[/tex]
[tex]\( y = [18, 12, -15, -45] \)[/tex]
- [tex]\( -6 \cdot 18 = -108 \)[/tex]
- [tex]\( -4 \cdot 12 = -48 \)[/tex]
- [tex]\( 5 \cdot -15 = -75 \)[/tex]
- [tex]\( 15 \cdot -45 = -675 \)[/tex]
The products are not constant.
Based on this analysis, the correct answer is:
b. B
