Question

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

Answer 1

8/5

Explanation:

Given that y varies directly with x , therefore ,

`\implies y \propto x`

Let k be the constant . Therefore ,

`\implies y = k x`

When the point is (5,8) ,

`\implies 8 = k * 5 \\\\\implies \underline{\underline{\boxed{ k =(8)/(5)}}}`

Hence the constant of variation is 8/5.

Answer 2

`(8)/(5)`

Explanation:

The constant of direction variation givens a proportion that is maintained by both x and y values for all points of a line that it passes through.

Usually represented with the variable
`k`, it is given by:

`(y)/(x)=k` for coordinates (x, y).

This relationship can be written as
`y=kx` which is also the layout for a proportional relationship.

Since coordinates are written (x, y), for point (5, 8), substitute
`x=5, y=8` to get the constant of variation:

`8=5k,\\k=\boxed{(8)/(5)}`