Question

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 :)

Answer 1

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