An approximate linear model that gives the remaining distance, in miles, a plane must travel from Los Angeles to Paris is given by
s(t) = 5500 − 500t
where s(t) is the remaining distance t hours after the flight begins. Find the intercepts on the vertical and horizontal axes.

To find the intercepts of the linear model \( s(t) = 5500 - 500t \), we need to determine both the vertical and horizontal intercepts.

1. **Vertical Intercept (s-axis)**:
   This occurs when \( t = 0 \):
   \[
   s(0) = 5500 - 500(0) = 5500
   \]
   Therefore, the vertical intercept is \( (0, 5500) \).

2. **Horizontal Intercept (t-axis)**:
   This occurs when \( s(t) = 0 \):
   \[
   0 = 5500 - 500t
   \]
   Solving for \( t \):
   \[
   500t = 5500 \quad \Rightarrow \quad t = \frac{5500}{500} = 11
   \]
   Therefore, the horizontal intercept is \( (11, 0) \).

### Summary of Intercepts:
- Vertical Intercept: \( (0, 5500) \)
- Horizontal Intercept: \( (11, 0) \)

Would you like more details or have any questions? Here are some related questions you might find interesting:

1. What does the slope of the line represent in this context?
2. How can we interpret the distance remaining after 5 hours?
3. What would the remaining distance be after 11 hours?
4. If the plane travels at a different speed, how would the equation change?
5. How can we graph this linear model?

**Tip:** When analyzing linear equations, the intercepts provide key insights into the relationship between the variables.

An approximate linear model that gives the remaining distance, in miles, a plane must travel from Los Angeles to Paris is given by s(t) = 5500 − 500t where s(t) is the remaining distance t hours after the flight begins. Find the intercepts on the vertical and horizontal axes.

Explore how to find the vertical and horizontal intercepts of the linear model s(t) = 5500 - 500t, which describes the remaining distance, in miles, of a plane traveling from Los Angeles to Paris. Learn key concepts of intercepts and linear equations, suitable for Grades 9-10.

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