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

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.

k=1.6

Step-by-step explanation:

Let us suppose

y=Kx

so satisfying the point

For

for

thus y varies linearly with x.

the answer is 40.

proof: