Question

A dolphin is 42 feet underwater and ascends at a constant rate for 14 seconds until it reaches the surface. Identify and interpret the intercepts for the situation.

Answer 1

Let us say that:

x = the time in seconds

y = depth of dolphin which is relative to the surface

The x intercept is located when y = 0, while the y intercept occurs when x = 0

We can see that at 0 seconds, the dolphin is still 42 feet below the surface:

x = 0, y = -42

The y intercept = -42 (0,-42)

After 14 seconds and at constant rate, the dolphin is now at the surface (0 below the surface):

x = 14, y = 0

The x intercept = 14 (14,0)

The slope is therefore m = (y2 - y1)/(x2 - x1) = 42/14 = 3.

Therefore, the formula for this line, in slope intercept form is

y = 3x - 42