Question

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Answer 1

Yes, y varies directly with x, and the equation is
`y=1.6x`.

Explanation:

To check where there is a direct relationship between x and y, we need to check whether all the x,y pairs we have fit some rule:

`y=k* x`.

For the first pair (x=4, y=6.4),

`6.4=k* 4`

Therefore
`k = 1.6`.

For the second pair (x=7, y=11.2),

`11.2=k* 7`

Therefore
`k = 1.6`.

For the third pair (x=10, y=16),

`16=k* 10`

Therefore
`k = 1.6`.

For the second pair (x=13, y=20.8),

`20.8=k* 13`

Therefore
`k = 1.6`.

So x does directly vary with y, and we have found out that
`k=1.6`.

Answer 2

Answer:
`\bold{(y)/(x)=1.6\quad \text{which is also equivalent to}\quad y=1.6x}`

Explanation:

`\begin {array}x&y&(y)/(x)=k\\--&--&-----\\4&6.4&(6.4)/(4)=1.6\\\\11.2&7&(11.2)/(7)=1.6\\\\10&16&(16)/(10)=1.6\\\\13&20.8&(20.8)/(13)=1.6\\\end{array}\\`

Since the k-value is the same for every value in the table, we can conclude that y varies directly with x and the constant of variation k = 1.6