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a coordinate plane shows quadrant 4 with the x-axis, labeled as minutes, ranging from 0 to 6 in increments of 1 and y-axis, labeled as elevation in feet, ranging from 0 to negative 110 in decrements of 10. A ray with arrow at the bottom end points downward from the origin. The coordinates that it passes through are left parenthesis 0 comma 0 right parenthesis, left parenthesis 3 comma negative 60 right parenthesis, and left parenthesis 5 comma negative 100 right parenthesis.

The graph shows the elevation of a deep-sea diver in relation to minutes passed. Using any two points on the graph, what is the rate of change in the diver’s elevation?

(1 point)
feet per minute
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1 answer

To determine the rate of change in the diver's elevation using two points from the graph, we can use the formula for the rate of change, which is given by:

\[ \text{Rate of Change} = \frac{\text{Change in Elevation}}{\text{Change in Time}} = \frac{y_2 - y_1}{x_2 - x_1} \]

Let's use the two points (0, 0) and (5, -100):

  • \( (x_1, y_1) = (0, 0) \)
  • \( (x_2, y_2) = (5, -100) \)

Now, we can calculate the change in elevation and time:

  • Change in elevation: \( y_2 - y_1 = -100 - 0 = -100 \) feet
  • Change in time: \( x_2 - x_1 = 5 - 0 = 5 \) minutes

Now we can plug these values into the rate of change formula:

\[ \text{Rate of Change} = \frac{-100}{5} = -20 \]

Thus, the rate of change in the diver's elevation is -20 feet per minute.