Question

The graph shows the depth, y, in meters, of a shark from the surface of an ocean for a certain amount of time, x, in minutes:Distance vs. TimeY189168147АDistance126from Ocean 105Surface(m)8463Bс42210 1 2 3 4Time (min)5Part A: Describe how you can use similar triangles to explain why the slope of the graph between points A and B is the same as the slope of the graph between points A and C. (4 points)Part B: What are the initial value and slope of the graph, and what do they represent? (6 points)B i UFont Family- AA- A=-=-=OCDܚ11+SAVE & EXIT

Answer 1

A) We can draw some vertical and horizontal lines to construct two similar triangles:

We now have two similar triangles: AEB and ADC.

The slope is the quotient between the variation in y and the variation in x.

Then, we can express the slope as:

`m=(AD)/(CD)=(AE)/(BE)`

As the triangles are similar, we can write the following proportions:

`k=(AE)/(AD)=(BE)/(CD)`

We can rearrange this as:

`\begin{gathered} (AE)/(AD)=(BE)/(CD) \\ AE\cdot CD=BE\cdot AD \\ (AE)/(BD)=(AD)/(CD) \end{gathered}`

and we get the same result from the slope m.

B) We can see that in the graph the initial value is y = 63.

This correspond to the y-intercept of the line, which is the value of the line when x = 0.

In this case, the initial value of y = 63 represents the initial distance from the ocean surface, in meters.

The slope is the rate of change of the distance from the surface per unit of time. In other words, the speed (in meters per minute) at which the shark is approaching the surface. In this case, the speed can be calculated as:

`\begin{gathered} m=(y_a-y_c)/(x_a-x_c) \\ m=(147-63)/(2-0)=(84)/(2)=42 \end{gathered}`

The speed is then 42 meters per minute.