Answered

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

x y

---------------------------

10 12

15 18

20 24


a.) yes; y=1.2x

b.) yes; y=2x

c.) yes; y=x+1

d.) no; y does not vary directly with x.

Verified Answer :

bcalle

The correct answer is A.

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 \(y=kx\)

Verify

A) For the point\((10,12)\)

Find the value of k

\(k=y/x\)

substitute

\(k=12/10=1.2\)

B) For the point\((15,18)\)

Find the value of k

\(k=y/x\)

substitute

\(k=18/15=1.2\)

C) For the point\((20,24)\)

Find the value of k

\(k=y/x\)

substitute

\(k=24/20=1.2\)

so

The value of k is equal to \(1.2\)

The equation of the direct variation is equal to

\(y=1.2x\)

therefore

the answer is the option a

yes; \(y=1.2x\)

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