Question

What is the constant of variation,k, of the direct variation,y=kx,through (5,8)

Answer 1

`\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------\\\\ (\stackrel{x}{5}~,~\stackrel{y}{8})\textit{ we also know that } \begin{cases} x=5\\ y=8 \end{cases}\implies 8=k5\implies \cfrac{8}{5}=k`

Answer 2

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form
`(y)/(x)=k` or
`y=kx`

where

k is the constant of variation

in this problem we have

the point
`(5,8)`

so

`x=5\\y=8`

substitute

`(y)/(x)=k`

`(8)/(5)=k`

therefore

the answer is

`k=(8)/(5)`