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:
Part 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.
Part B: What are the initial value and slope of the graph, and what do they represent? (6 points) Please try to explain it as simply as possible

Note that the graph depict the depth, y, in meters, of a shark that moves from the surface of an ocean for a given amount of time, x, in minutes.

So:

Part A :

We look at the two right triangles: Δ ABD and Δ BCE, and where D(2,100) and E(1,60) points.

Since the triangle are the same and thus, the slope of line segment AB: tan θ = AD/BD

= 140 - 100 / 2 - 1

= 40

Since the the slopes of line segment BC will be:

tan a = BE/CE

= 100 - 6 / 1 - 0

= 40

So, θ = α and the slope of AB and BC are similar.

Part B :

Using the graph, one can see that the initial value of the graph is 60 m and it stands for the initial position of the shark

e.g. at point t = 0 min, the shark was seen at a depth of 60 m from the water surface.

So therefore, since the slope of the graph is 40 it implies that the rate of change of distance from the Ocean surface of the shark in regards to the time in minutes have to be 40 m per min.

Therefore, The answers are:

Part A: The slope of AB and BC are the same.

Part B :The initial value is 60 m and the slope is 40 m/min.

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