1. Emily filled an empty horse trough with water. The water level, in centimeters, is proportional to time elapsed, in minutes, since she began filling the trough. The graph shows this relationship. (above)

(a) What rate does the point (8, 28) represent? Explain.

(b) Write the unit rate for the situation in terms of centimeters/minute? Explain how you found the unit rate.

(c) Explain how the points (8, 28) and (6, 21) show that the water level varies directly with the time elapsed.

For this graph, the rate at point (8,28) represents that at 8 min, the water level is at 28 cm. The unit rate for this situation is 3.5 centimeters per minute, which given in the equation y=3.5x, but can also be calculated using the given points. The points (8,28) and (6,21) shows that the water level and time elapsed are proportional because the change in distance between the two points is 3.5.

Step-by-step explanation:

The scenario and graph given represent a linear function. As the name indicates, the data will make a 'line', which can only happen when the data shows a consistent (or the same) change each time. So, if you look at the points on the graph and the points given, for each minute on the x-axis (Time) there is a 3.5 increase on the y-axis (Water Level). This is also given to you in the problem as the equation y=3.5x, where 3.5 represents the rate, x is the value of Time and y is the value of the Water Level. For each minute (x=1, x=2, etc.), you would multiply the x by 3.5 and that will give you the value of y, or the water level.