Question

select the correct answer.

patty buys a new car and gets it appraised every few years. after owning the car for 3 years, its value is $15,000. after owning the car for 5 years, its value is $9,000.

which equation represents this inverse variation?

\\(y = \frac{45,000}{x}\\)

\\(y = \frac{x}{45,000}\\)

\\(y = 15,000x\\)

\\(y = \frac{15,000}{x}\\)

Explanation:

Set up the inverse variation equation

$$ y = \frac{k}{x} \quad \text{or} \quad k = x \cdot y $$

Calculate the constant of variation

$$ k = 3 \cdot 15,000 = 45,000 $$

$$ k = 5 \cdot 9,000 = 45,000 $$

Write the final equation

$$ y = \frac{45,000}{x} $$

Answer:

• (A) \(y = \frac{45,000}{x}\) (Correct answer)
• (B) \(y = \frac{x}{45,000}\)
• (C) \(y = 15,000x\)
• (D) \(y = \frac{15,000}{x}\)