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:

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. (4 points)
Part B: What are the initial value and slope of the graph, and what do they represent?

Answer 1

Explanation:

Part A

Let the triangles be ADC and BEC.

Point D has coordinates of (0, 154), point E has coordinates of (0, 110).

The triangles have dimensions as below

ΔADC

• ⇒ base AD = 2, height DC = 154 - 66 = 88

The slope of AC

• ⇒ m = DC/AD = 88/2 = 44

ΔBEC

• ⇒ base BE = 1, height EC = 110 - 66 = 44

The slope of BC

• ⇒ m = EC/BE = 44/1 = 44

As we can see the slopes are equal

Part B

The y-intercept or initial value is represented by the point C and has coordinates of (0, 66)

The line is:

• y = 44x + 66

The initial value is the depth of 66 m where the shark is.

The slope is the 44 m increase of the depth every minute.