Question

The depth of the submarine is 50 feet below sea level when it starts to descend at the rate of 10.5 ft/s. It dives at that rate for 5 seconds. You want to model this descent with a linear equation. Determine the slope and the y-intercept. A) Slope: -10.5 ft/s, Y-Intercept: 50 ft

B) Slope: 10.5 ft/s, Y-Intercept: -50 ft
C) Slope: -50 ft, Y-Intercept: 10.5 ft/s
D) Slope: 50 ft, Y-Intercept: -10.5 ft/s

Answer 1

The slope of the linear equation that models the submarine's descent is -10.5 ft/s, and the y-intercept is -50 feet below sea level. Therefore, the correct answer is B) Slope: 10.5 ft/s, Y-Intercept: -50 ft.

Step-by-step explanation:

The submarine's rate of descent at 10.5 ft/s represents the slope of the linear equation since it is the rate of change in depth per second. The starting point, 50 feet below sea level, serves as the y-intercept because it is the depth at which the descent begins when time is zero seconds.

To model this situation as a linear equation y = mx + b, where y is the depth in feet, x is the time in seconds, m is the slope, and b is the y-intercept, we can set m to be -10.5 and b to be -50. Therefore, the slope is -10.5 ft/s, and the y-intercept is -50 ft, which corresponds to answer choice B.