Question

A motor boat moves across a lake at a constant speed. when it begins, is is 64 km from the shore after 17 minutes, it is 30 km from the shore.

Which function describes the motor boats distance from the shore?
A. y = 2x + 64
B. y = -2x + 64
C. y = -17x + 30
D. y = 17x + 64

Answer 1

The function that describes the motor boat's distance from the shore is y = -2x + 64.

Step-by-step explanation:

The function that describes the motor boat's distance from the shore is option B, y = -2x + 64.

To determine the equation, we need to consider the relationship between distance, time, and speed. We know that the motor boat moves at a constant speed. When it begins, it is 64 km from the shore. After 17 minutes, it is 30 km from the shore.

We can set up a linear equation where x represents the time in minutes and y represents the distance from the shore. Using the two data points, we can solve for the equation.

First data point: (0, 64)

Second data point: (17, 30)

Using the point-slope formula, we can calculate the equation:

y - y1 = m(x - x1)

Where m is the slope and (x1, y1) is any point on the line.

Using the formula, we get:

y - 64 = -2(x - 0)

y - 64 = -2x

y = -2x + 64

Therefore, the function that describes the motor boat's distance from the shore is y = -2x + 64.