Question

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

x|y 10|15 16|24 20|30
A. Yes; y=1.5x
B. Yes; y=2x
C. Yes; y=x+5
D. No there is no direct variation.

2. For the data table, does y vary directly with x? If it does, write equation for the direct variation.
x|y 32|24 16|8 8|6
A. Yes; y=0.5x
B. Yes; y=2x
C. Yes; y=1.5x
D. No there is no direct variation.

Thank you!

Answer 1

Part 1) Option A. Yes; y=1.5x

Part 2) Option D. No there is no direct variation

Explanation:

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`

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Part 1) we have the points

(10,15),(16,24),(20,30)

Find the value of the constant of proportionality k

`k=y/x`

For x=10, y=15

substitute

`k=15/10=1.5`

For x=16, y=24

substitute

`k=24/16=1.5`

For x=20, y=30

substitute

`k=30/20=1.5`

The value of the constant k is the same for the three ordered pairs

The linear equation is
`y=1.5x`

therefore

y vary directly with x

Part 2) we have the points

(32,24),(16,8),(8,6)

Find the value of the constant of proportionality k

`k=y/x`

For x=32, y=24

substitute

`k=24/32=0.75`

For x=16, y=8

substitute

`k=8/16=0.5`

For x=8, y=6

substitute

`k=6/8=0.75`

The value of the constant k is not the same for the three ordered pairs

therefore

y not vary directly with x