Question

05.09 Module Five Test Part TwoMega 924162 / Mote SURNOSClevelandThe grh the depthy, in meters of share from the surface of an ocean forsetin amount of time in minutesPart A Decribe how you can use similar triangles to explains why the slope of the graph between points A and B la the same as the slope of the graphs between points and taPerte. What are the initialyslue and slope of the graph, and what do they represent? (6 ponta)BU Font Family• A AMINT ALEAHO

Answer 1

A) the ratio of corresponding sides are equal. This makes the slopes equal

see explanation below

B) i) The initial value is 63

ii) The slope of the graph is 42

The initial depth of the shark from the ocean surface is 63 meters

The shark moves at a rate of 42 meters/minutes

Step-by-step explanation:

Part A

In similar triangles or shapes, the ratio of corresponding sides are equal

From the graph:

Distance AB corresponds to AC.

Distance AC = Distance AB × scale factor

scale factor = Distance AC/ Distance AB

The ratio of their distance will be equal to a constant

As a result, the ratio of their slope will also be equal

let's find slope AB and AC respectively

A (2, 147), B (1, 105) and C (0, 63)

To get the slope, we will apply the slope formula:

`m\text{ = }(y_2-y_1)/(x_2-x_1)`
`\begin{gathered} \text{slope AB: }x_1=2,y_1=147,x_2=1,y_2\text{ = 1}05 \\ m\text{ = }\frac{105\text{ - 147}}{1\text{ - 2}} \\ m\text{ = }(-42)/(-1) \\ \text{slope AB = m = }42 \end{gathered}`
`\begin{gathered} \text{slope AC: }x_1=2,y_1=147,x_2=0,y_2\text{ = }63 \\ m\text{ = }(63-147)/(0-2) \\ m\text{ = }(-84)/(-2) \\ \text{slope AC = m = 42} \end{gathered}`

Slope AB = Slope AC

Part B:

The initial value of the graph is the value of y when x = 0

Tio locate the initial value on the graph, we check for the value of y when the lines crosses the y axis.

The line crosses the y axis at y = 63

The initial value is 63

Since slope AB = slope AC = 42

The slope of the grapg is 42

The initial value represents the initial depth of the shark from the ocean surface.

The initial depth of the shark from the ocean surface is 63 meters

The slope represents the rate of change of the shark's distance from the ocean surface.

The shark moves at a rate of 42 meters/minutes