a) Marco is driving to the Grand Canyon. His distance from the Grand Canyon decreases 150 mi every 3 h . After 4 h , his distance from the Grand Canyon is 200 mi . Marco's distance from the Grand Canyon in miles, \( y \), is a function of the number of hours he drives, \( x \). (4)) What is the rate of change? Find the change in Marco's distance each hour. (4) What is the initial value? Find Marco's distance from the Grand Canyon when he starts to drive. (4nitial value:

We know that Marco’s distance decreases 150 miles every 3 hours. To find the rate of change each hour: 1. Rate of Change:   Divide 150 miles by 3 hours to get 50 miles per hour. Since the distance is decreasing, the rate of change is –50 miles per hour. 2. Initial Value:   Let y represent the distance from the Grand Canyon and x be the number of hours driven. The distance function is of the form:     y = initial distance + (rate of change)·x.   After 4 hours, y = 200 miles:     200 = (initial value) + (–50)(4).   This simplifies to:     200 = initial value – 200.   Solving for the initial value:     initial value = 200 + 200 = 400 miles. Thus, Marco's distance from the Grand Canyon when he starts driving is 400 miles.