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  1. For the data in the table does y vary directly with x? If it does write an equation for the direct variation.

x|y 8|28 16|56 20|70 a. yes;y=5x b. yes;y=x+20 c. yes;y=3.5x d. no; y doesn't vary directly with x 2. For the data in the table does y vary directly with x? If it does write an equation for the direct variation.

x|y 40|32 28|16 16|12 a. no;y does not vary directly with x b. yes; y=2x c. yes; y=1.5x d. yes; y=0.2x Please answer whenever you get the chance. I really need help on this. thank you :)

Verified Answer :

calculista

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form \(y/x=k\) or \(y=kx\)

Part 1)

Find the value of k for each data in the table

a) For the point\((8,28)\)

\(k=y/x\)

\(k=28/8=3.5\)

b) For the point\((16,56)\)

\(k=y/x\)

\(k=56/16=3.5\)

c) For the point\((20,70)\)

\(k=y/x\)

\(k=70/20=3.5\)

therefore

the value of k is equal for the three points in the data set

so

the data represent a direct variation

the equation is equal to

\(y=3.5x\)

therefore

the answer Part 1) is the option C

yes; \(y=3.5x\)

Part 2)

Find the value of k for each data in the table

a) For the point\((40,32)\)

\(k=y/x\)

\(k=32/40=0.8\)

b) For the point\((28,16)\)

\(k=y/x\)

\(k=16/28=0.57\)

c) For the point\((16,12)\)

\(k=y/x\)

\(k=12/16=0.75\)

therefore

the value of k is different for the three points in the data set

so

the data not represent a direct variation

therefore

the answer Part 2) is the option A

no;y does not vary directly with x

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