Does this table show a proportional relationship between x and y?

Yes there is a direct proportional relationship between x and y.

Explanation:

Direct proportional relationship equations are of the form y = kx

In the first row we have x = 3 and y = 2 pair up. So if y = kx, then,

y = kx

2 = k*3

2/3 = k

k = 2/3

Making the equation y = (2/3)x

Let's try the second row with this new equation. Plugging in x = 6 should lead to y = 4

Let's find out

y = (2/3)x

y = (2/3)*6

y = (2/3)*(6/1)

y = (2*6)/(3*1)

y = 12/3

y = 4

So this verifies the second row. The third row will be similar

y = (2/3)x

y = (2/3)*9

y = 6

I'll let you verify the fourth row. You should find that x = 12 leads to y = 8

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step-by-step explanation: