Question: Which equation shows inverse variation? Choose 1 answer: A) \( a = \frac{1}{9} \cdot b \) B)…

Which equation shows inverse variation?

Choose 1 answer:

A) \( a = \frac{1}{9} \cdot b \)

B) \( \frac{a}{b} = \frac{1}{9} \)

C) \( \frac{a}{b} = 9 \)

D) \( a = \frac{1}{9} \cdot \frac{1}{b} \)

E) \( 9 \cdot a = b \)

Solution

Inverse variation is expressed as \( a \cdot b = k \), where \( k \) is a constant. Let’s look at the options: A) \( a = \frac{1}{9} \cdot b \) B) \( \frac{a}{b} = \frac{1}{9} \) C) \( \frac{a}{b} = 9 \) D) \( a = \frac{1}{9} \cdot \frac{1}{b} \) E) \( 9 \cdot a = b \) For option D: Rewrite the equation: \[ a = \frac{1}{9} \cdot \frac{1}{b} \] Multiply both sides by \( b \): \[ a \cdot b = \frac{1}{9} \] This fits the form of inverse variation, where \( k = \frac{1}{9} \). Therefore, the correct answer is D.