Answer:
A, B and C
Step-by-step explanation:
In the equation: 3y=27x
Making y the subject of the equation, we have:
The constant of proportionality between y and x is 9.
We want to determine which relationships have the same constant of proportionality 9.
<u>Option A</u>
y=9x
The constant of proportionality is 9.
<u>Option B</u>
2y=18x
Divide both sides by 2 to obtain: y=9x
The constant of proportionality is 9.
<u>Option C</u>
x=3, y=1/3
Substitution into y=kx gives:
1/3=3k
k=9
The constant of proportionality is 9.
<u>Option D</u>
x=6, y=2/3
Substitution into y=kx gives:
2/3=6k
k=2/3*6=4
The constant of proportionality is 4.
<u>Option E</u>
When x=2, y=18
Substitution into y=kx gives:
18=2k
k=9
However, when x=4, y=27
Substitution into y=kx gives:
27=4k
k=6.75
This is not a proportional relation since the constant of proportionality is not equal.
The correct options are A, B and C