contestada

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.

Respuesta :

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 [tex]y/x=k[/tex] or [tex]y=kx[/tex]

Verify

A) For the point[tex](10,12)[/tex]

Find the value of k

[tex]k=y/x[/tex]

substitute

[tex]k=12/10=1.2[/tex]

B) For the point[tex](15,18)[/tex]

Find the value of k

[tex]k=y/x[/tex]

substitute

[tex]k=18/15=1.2[/tex]

C) For the point[tex](20,24)[/tex]

Find the value of k

[tex]k=y/x[/tex]

substitute

[tex]k=24/20=1.2[/tex]

so

The value of k is equal to [tex]1.2[/tex]

The equation of the direct variation is equal to

[tex]y=1.2x[/tex]

therefore

the answer is the option a

yes; [tex]y=1.2x[/tex]

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