A company developed the following linear model to help budget annual expenses over time. In this model, x represents the number of years after 2009, and y represents the expense budget (in dollars). Interpret the y-intercept.

Question

A.
The company's expense budget for 2009 was $37,896.
B.
The company's expense budget for 2009 was $189,785.
C.
The company's expense budget for 2008 was $189,785.
D.
The company's expense budget for 2008 was $37,896.

Answer 1

To interpret the y-intercept in a linear model where \( x \) represents the number of years after 2009, you need to find the value of \( y \) when \( x = 0 \).

When \( x = 0 \), it corresponds to the year 2009. Thus, the y-intercept represents the expense budget for the year 2009.

Therefore, if the y-intercept is \($37,896\), the correct interpretation would be:

A. The company's expense budget for 2009 was $37,896.

If the y-intercept were \($189,785\), the correct interpretation would be:

B. The company's expense budget for 2009 was $189,785.

Without seeing the exact equation or y-intercept value, we can't definitively state which option is correct, but the interpretation itself is always that it reflects the budget for the year 2009.

So, the correct choice for interpreting the y-intercept in general is:

The company's expense budget for 2009 (depending on the value of the intercept).