Question

After 2 minutes, a submarine had descended to −590 feet. After 6 minutes, the submarine had descended to −630 feet. Assuming a linear function, write an equation in the form d(t)=mt+b that shows the depth, d(t), after t minutes. Provide your answer below:

Answer 1

d(t) = -10t - 570

Explanation:

To write an equation in the form d(t) = mt + b that represents the depth of the submarine after t minutes, we need to determine the values of m and b.

We are given two points: (2, -590) and (6, -630), which represent the time in minutes and the corresponding depth in feet. We can use these points to find the slope, m, and the y-intercept, b, of the linear function.

To find the slope, we can use the formula:

m = (change in y) / (change in x)

m = (-630 - (-590)) / (6 - 2)

m = -40 / 4

m = -10

The slope of the function is -10.

To find the y-intercept, we can substitute the values of one of the given points into the equation and solve for b. Let's use the point (2, -590):

-590 = -10(2) + b

-590 = -20 + b

b = -590 + 20

b = -570

The y-intercept, b, is -570.

Therefore, the equation in the form d(t) = mt + b that represents the depth, d(t), after t minutes is:

d(t) = -10t - 570