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