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. (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. Answer:

A rate is the ratio between some dependent value and the corresponding independent value. When time is involved, it is usually taken to be the independent value.

The point represents 8 minutes and 28 cm, so the rate is ...

... (28 cm)/(8 min) = 3 1/2 cm/min

(b)

A unit rate is a rate with one (1) unit of the independent variable in the denominator. The unit rate here is 3 1/2 cm/min. (1 minute is the denominator.)

A unit rate is found by dividing the dependent quantity by the independent quantity and simplifying the numbers so there is one independent unit in the denominator.

(c)

(21 cm)/(6 min) = 3 1/2 cm/min, the same rate as when the depth is 28 cm. In graphical terms, both points are on a line through the origin, which means the relationship is a proportional one.