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 [tex]y/x=k[/tex] or [tex]y=kx[/tex]
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
[tex]k=y/x[/tex]
For x=10, y=15
substitute
[tex]k=15/10=1.5[/tex]
For x=16, y=24
substitute
[tex]k=24/16=1.5[/tex]
For x=20, y=30
substitute
[tex]k=30/20=1.5[/tex]
The value of the constant k is the same for the three ordered pairs
The linear equation is [tex]y=1.5x[/tex]
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
[tex]k=y/x[/tex]
For x=32, y=24
substitute
[tex]k=24/32=0.75[/tex]
For x=16, y=8
substitute
[tex]k=8/16=0.5[/tex]
For x=8, y=6
substitute
[tex]k=6/8=0.75[/tex]
The value of the constant k is not the same for the three ordered pairs
therefore
y not vary directly with x
