3. 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 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 0,60, b at ordered pair 1, 100, a at ordered pair 2, 140, and the ordered pair 3, 180. 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)

PART A
Since the graph described will form a straight line, the concept of similar triangles can be used when comparing the slopes on AB and AC. We just imagine a triangle formed by the line segments and their corresponding x and y components. We can notice that their angles don't actually change so we know that the two triangles formed are proportional. This would mean that getting the slope (Δy/Δx) would yield us the same number.

PART B
The initial value of the graph is 60 meters and this represents the initial position of the shark (it is located 60 meters below the ocean surface).

The slope of the graph is  and this represents how fast (speed) the shark can dive. We know this because dividing meters over the number of minutes would give us meters/minute and this is describing the speed.