Given that 𝑦 varies directly as 𝑥, write an equation for 𝑦 in terms of 𝑥 using 𝑘 as a nonzero constant.
As 𝑦 and 𝑥 vary directly, we can say that 𝑦 is proportional to 𝑥. This means as 𝑥 increases, so does 𝑦. If we let 𝑘 be the factor or constant of proportionality, we can rewrite this as 𝑦 equals 𝑘 multiplied by 𝑥.
Our value of 𝑦 will increase directly in relation to our value of 𝑥 with a gradient of 𝑘. If 𝑦 was varying directly as 𝑥 squared instead of 𝑥, we could rewrite this equation as 𝑦 equals 𝑘 multiplied by 𝑥 squared.
In a similar way, if 𝑦 varied directly as 𝑥 cubed, our equation would be 𝑦 equals 𝑘 multiplied by 𝑥 cubed.