Given that 𝑦 varies directly as 𝑥
squared, write an equation for 𝑦 in terms of 𝑥 using 𝑘 as a nonzero constant.
If two variables vary directly, we
can say that they are in direct proportion to one another. This means that as one value
increases, so does the other. Our two variables are 𝑦 and 𝑥
squared, which means that 𝑦 is directly proportional to 𝑥 squared. This also means that the ratio or
quotient of the two variables is equal to some constant 𝑘. 𝑦 divided by 𝑥 squared is equal
to 𝑘. We can make 𝑦 the subject of this
equation by multiplying both sides by 𝑥 squared. 𝑦 is therefore equal to 𝑘
multiplied by 𝑥 squared.
When dealing with questions of this
type, we usually go from the proportion expression to our final answer. We replace the proportion symbol
with an equal symbol and a constant 𝑘. If 𝑦 varies directly as 𝑥
squared, then 𝑦 is equal to 𝑘 multiplied by 𝑥 squared.