Question

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?

Explanation:

Step1: Identify two points

From the graph, let's take two points. Let's assume at \( x = 0 \) (minutes), \( y=-20 \) (feet) and at \( x = 2 \) minutes, \( y=-40 \) feet. (We can also use other points, but these are clear from the grid.)

Step2: Calculate rate of change (slope)

The formula for rate of change (slope) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Let \( (x_1,y_1)=(0, - 20) \) and \( (x_2,y_2)=(2,-40) \). Then \( m=\frac{-40-(-20)}{2 - 0}=\frac{-20}{2}=-10 \). Let's check with another pair, say \( (0,-20) \) and \( (3,-50) \). \( m=\frac{-50 - (-20)}{3-0}=\frac{-30}{3}=-10 \). So the rate of change is -10 feet per minute.

Answer:

-10 feet per minute