𝑦 is inversely proportional to 𝑥. Circle the letter of the graph which shows this relationship.
If two variables are inversely proportional to one another, that means that as one increases, the other decreases. We use the symbol 𝛼 to mean “is proportional to.” So if 𝑦 is inversely proportional to 𝑥, we can say that 𝑦 is proportional to one over 𝑥. We can form an equation. And more specifically, we say that 𝑦 is equal to some constant 𝑘 over 𝑥. 𝑘 is sometimes called the constant of proportionality. And we can also say that this is a reciprocal relationship. We need to be able to recognise a reciprocal graph.
A reciprocal graph 𝑦 is equal to 𝑎 over 𝑥, where 𝑎 is a positive constant, looks like this. When investigating proportionality, we’re actually only interested in the positive values. And we can now say that we’re interested in the graph A. In fact, the only other graph that represents a proportional relationship is D. This is a graph that shows 𝑦 is being directly proportional to 𝑥. And we say that 𝑦 is equal to 𝑘 multiplied by 𝑥, where 𝑘 is some constant.
The letter of the graph which shows 𝑦 being inversely proportional to 𝑥 is A.