Answer: Choice A) y = (-1/3)x
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Explanation:
Since x and y are in a proportional relationship, this means that y = kx. This is a direct variation equation.
k is the proportionality constant
To find k, we'll use any nonzero x and y pairing. Let's say we use the second row with x = -3 and y = 1
This leads to
y = kx
y/x = k
k = y/x
k = 1/(-3)
k = -1/3
Or we could use the third row to get
k = y/x
k = 2/(-6)
k = (1*2)/(-3*2)
k = -1/3
We get the same value of k for that row as well. I'll let you check the other rows. You cannot use the first row because dividing by zero is not allowed.
Since k = -1/3, this means y = kx updates to y = (-1/3)x which matches with choice A. So effectively, whatever the x input is, we multiply that by -1/3 to get the y output.
Multiplying by -1/3 is the same as dividing by -3. This means that y = (-1/3)x is the same as y = -x/3
