Question 9 (4 points)

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The value in dollars, y, of a boat x years after it was purchased can be modeled by the function
y=36,000-900x

What does the y-intercept mean in this equation?

Question 9 options:

The original value of the boat was $36,000

The value of the boat after x years

The number of years, x, until the boat reaches half its original value

The value of the boat decreases by $900 each year

Answer 1

The y-intercept of the equation \( y = 36,000 - 900x \) occurs when \( x = 0 \). Substituting \( x = 0 \) into the equation gives:

\[ y = 36,000 - 900(0) = 36,000 \]

This indicates that when the boat is just purchased (0 years after purchase), its value is $36,000.

Therefore, the correct interpretation of the y-intercept in this equation is:

The original value of the boat was $36,000.