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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

Respuesta :

sqdancefan

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.

Answer:k=1.6

Step-by-step explanation:

Let us suppose

y=Kx

so satisfying the point [tex]\left ( 4,6.4\right )[/tex]

[tex]k=\frac{6.4}{4}=1.6[/tex]

[tex]For \left ( 7,11.2\right )[/tex]

[tex]k=\frac{11.2}{7}=1.6[/tex]

For [tex]\left ( 10,16\right )[/tex]

[tex]k=\frac{16}{10}=1.6[/tex]

for [tex]\left ( 13,20.8\right )[/tex]

[tex]k=\frac{20.8}{13}=1.6[/tex]

thus y varies linearly with x.

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