The initial distance and direction of movement, the function A. y = -9x + 50 accurately describes the motorboat's distance from the shore. Therefore , A. y = -9x + 50 is correct .
Here's why:
y: represents the motorboat's distance from the shore in kilometers.
x: represents the time in minutes that have passed since the journey began.
Slope: -9 represents the motorboat's speed. A negative slope indicates the distance is decreasing (moving towards the shore) with time.
Y-intercept: 50 represents the starting distance from the shore, which is given as 50 km.
Let's analyze the other options:
B. y = 4x + 50: This would imply the boat is moving away from the shore with a positive speed, which is not the case.
C. y = -4x + 50: This has the correct negative slope but a slower speed (-4 km/min) compared to the given information.
D. y = 9x + 50: This has the same speed as option A but the wrong sign for the slope, suggesting it's moving away from the shore.
Therefore, based on the initial distance and direction of movement, the function y = -9x + 50 accurately describes the motorboat's distance from the shore.