Question Video: Identifying the Constant of Proportionality in Equations Mathematics • 7th Grade

The amount of meat required to feed a captive lion is given by the equation 𝑤 = 9𝑑, where 𝑤 is the weight of the meat in kilograms needed to feed a lion for 𝑑 days. What is the unit rate of this proportional relationship?

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Video Transcript

The amount of meat required to feed a captive lion is given by the equation 𝑤 equals nine 𝑑, where 𝑤 is the weight of the meat in kilograms needed to feed a lion for 𝑑 days. What is the unit rate of this proportional relationship?

𝑤 and 𝑑 are our two variables here; they are said to be in direct variation to one another. In other words, when 𝑑 increases, the number of days which the lion is required to be fed on, 𝑤, the weight of the meat required, will also increase. So, what do we mean when we talk about the unit rate of the proportional relationship?

Consider the variables 𝑦 and 𝑥 that are directly related to one another. We say 𝑦 is equal to 𝑘 times 𝑥, where 𝑘 is said to be the constant of variation. The constant of variation tells us how much 𝑦 increases by when 𝑥 increases by one. In other words, we can think about 𝑘 as being the constant of variation.

So, in the equation 𝑤 equals nine 𝑑, nine must be the constant of variation. It must be the unit rate. But what exactly does it represent? If we represent this on a graph, we know that as the number of days increase, so does the weight of the meat required. In fact, each day the amount of meat required will increase by nine kilograms. So, the unit of the number nine is kilograms per day.

So, the unit rate of the proportional relationship then is nine kilograms per day.