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Answer:

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

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

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form or

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

For x=10, y=15

substitute

For x=16, y=24

substitute

For x=20, y=30

substitute

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

The linear equation is

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

For x=32, y=24

substitute

For x=16, y=8

substitute

For x=8, y=6

substitute

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

therefore

y not vary directly with x