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: What is the slope of the graph between points A and B? And between points A and C? explain your reasoning (4 points)
Part B: What is the initial value and what doesit represent? (6 points)
Part A: To find the slope between two points on a graph, we can use the formula:
slope = (change in y) / (change in x)
Between points A and B, the change in y is 100 - 140 = -40, and the change in x is 1 - 2 = -1.
slope AB = (-40) / (-1) = 40
Between points A and C, the change in y is 60 - 140 = -80, and the change in x is 0 - 2 = -2.
slope AC = (-80) / (-2) = 40
The slope of the graph between points A and B and between points A and C is 40. This means that for every 1 minute increase in time, the shark descends 40 meters in depth.
Part B: The initial value of the graph is the y-coordinate of the point where the line intersects the y-axis (x = 0). In this case, at point C, the y-coordinate is 60.
The initial value represents the starting depth of the shark from the ocean surface. So, the initial value of 60 meters means that the shark is initially 60 meters below the surface of the ocean.