Final answer:
To determine the function describing the motorboat's distance from the shore, we use the two points (0, 50) and (9, 14) to calculate the slope of the linear function. The slope is found to be -4 km/min, indicating the boat is moving towards the shore at that rate. Thus, the distance function is y = -4x + 50, where y is the distance from the shore and x is the time in minutes.
Step-by-step explanation:
Finding the Function Describing the Motorboat's Distance from the Shore
To determine the function that describes the motorboat's distance from the shore, we need to consider the information given. The motorboat starts 50 km away from the shore and after 9 minutes, it's 14 km from the shore. Since the boat is moving at a constant speed, we can assume a linear function for the distance covered over time.
The general form of a linear function is:
y = mx + b
Where:
- y is the distance from the shore in kilometers
- m is the slope of the line, which represents the speed of the boat in km/min
- x is the time in minutes
- b is the y-intercept, which in this case is the initial distance from the shore (50 km)
We know two points on this line: (0, 50) and (9, 14). To find the slope (m), we can use the formula:
m = (y2 - y1) / (x2 - x1)
Substituting in our values, we get:
m = (14 - 50) / (9 - 0) = -36 / 9 = -4
The slope is -4 km/min, which means the boat is moving towards the shore at a rate of 4 km every minute. Now we can write the function as:
y = -4x + 50
This function describes the motorboat's distance from the shore as a function of time.