Question

Determine whether y varies directly with x. If so find the constant of variation k and write the equation. X 4,7,10,13. Y 6.4,11.2,16,20.8

Answer 1

Answer:k=1.6

Explanation:

Let us suppose

y=Kx

so satisfying the point
`\left ( 4,6.4\right )`

`k=(6.4)/(4)=1.6`

`For \left ( 7,11.2\right )`

`k=(11.2)/(7)=1.6`

For
`\left ( 10,16\right )`

`k=(16)/(10)=1.6`

for
`\left ( 13,20.8\right )`

`k=(20.8)/(13)=1.6`

thus y varies linearly with x.

Answer 2

Direct variation is modeled by

... y = k·x

Then the value of k can be found by finding the ratio of any corresponding pair of numbers from your table. I find it convenient to choose the one where x=10, so the math is easy to do mentally.

... y/x = k

... 16/10 = k = 1.6

Then the equation is

... y = 1.6x

_____

Checking the other values in the table, we find that this equation fits all of them, so you do have direct variation.