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: A graph is titled Distance Vs. Time is shown. The x axis is labeled Time in minutes and shows numbers 0, 1, 2, 3, 4, 5. The y axis is labeled Distance from Ocean Surface in meters. A straight line joins the points C at ordered pair 0,66, B at ordered pair 1, 110, A at ordered pair 2, 154, and the ordered pair 3, 198. 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? (6 points) Source StylesNormal

Answer 1

Step-by-step explanation

Step 1

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

the slope of a line ( or segment) is given by:

`\text{slope}=\frac{change\text{ in y }}{\text{change in x}}=(y_2-y_1)/(x_2-x_1)`

we can see , in both cases ( slope of AB and slope of AC) is the same

then, replace

`\text{slope}=\frac{change\text{ in y }}{\text{change in x}}`

`\begin{gathered} slope_(AB)=\frac{2(\text{blue)}}{1(\text{red)}}=2 \\ Slope_(AC)=\frac{4(\text{yellow)}}{2(\text{purple)}}=2 \end{gathered}`

so, as ratio of the change i y to the change in x in the triangles is the same , the slope is the same

Step 2

What are the initial value and slope of the graph, and what do they represent?

a) Slope:

as we found in the previous step,the slope of the line is 2

`\text{slope}=\frac{change\text{ in y }}{\text{change in x}}=\frac{change\text{ in distance}}{\text{change in time}}`

according to the units in the axes, the slope is the ratio of change in distance to the change in time, it is know as speed

b) the iniitial value, is the distance for time=0, we can easily found this on the graph by checking the point where the lines intersectsthe y-axis

therefore, the initial value is 66

it means the shark was 66 under the surface at time t = 0

I hope this helps you