Functions Unit Test

Question

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Question
Use the image to answer the question.

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

Answer 1

To calculate the rate of change in the diver's elevation, we can use the two points provided:

1. \( (3, -60) \) which means after 3 minutes, the elevation is -60 feet.
2. \( (5, -100) \) which means after 5 minutes, the elevation is -100 feet.

The formula to find the rate of change is:

\[ \text{Rate of change} = \frac{\text{Change in elevation}}{\text{Change in time}} = \frac{y_2 - y_1}{x_2 - x_1} \]

Substituting the coordinates into the formula:

• First point: \( (3, -60) \) ➔ \( x_1 = 3 \), \( y_1 = -60 \)
• Second point: \( (5, -100) \) ➔ \( x_2 = 5 \), \( y_2 = -100 \)

Now, calculate the change in elevation:

\[ y_2 - y_1 = -100 - (-60) = -100 + 60 = -40 \]

Next, calculate the change in time:

\[ x_2 - x_1 = 5 - 3 = 2 \]

Now we can find the rate of change:

\[ \text{Rate of change} = \frac{-40}{2} = -20 \text{ feet per minute} \]

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