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
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:
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\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{ = }\frac{-42}{-1} \\ \text{slope AB = m = }42 \end{gathered}[/tex][tex]\begin{gathered} \text{slope AC: }x_1=2,y_1=147,x_2=0,y_2\text{ = }63 \\ m\text{ = }\frac{63-147}{0-2} \\ m\text{ = }\frac{-84}{-2} \\ \text{slope AC = m = 42} \end{gathered}[/tex]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