Question

After 1 minute, a submarine had descended to -280 feet. After 9 minutes, the submarine had descended to -360 feet. Assuming a linear function, write an equation in the form d(t)=mt+b that shows the depth, d(t), after t minutes. a) d(t) = -40t - 280 b) d(t) = -20t - 280 c) d(t) = -10t - 280 d) d(t) = -40t - 360

Answer 1

The linear equation that represents the depth of the submarine after t minutes is d(t) = -10t - 280, calculated by finding the slope between two given points and knowing the y-intercept is -280 from the first point. option c is correct.

Step-by-step explanation:

To find the equation of the linear function that shows the depth, d(t), of a submarine after t minutes, we can use the given points: (1, -280) and (9, -360). The slope (m) is the change in depth over the change in time, which can be calculated as:

m = (Depth2 - Depth1) / (Time2 - Time1)

m = (-360 - (-280)) / (9 - 1)

m = (-360 + 280) / 8

m = -80 / 8

m = -10

The y-intercept (b) is the depth at time t = 0, which based on the first data point, is -280.

Therefore, our equation is d(t) = -10t - 280.

Hence, option c is correct.