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Answer: Choice A</h3>
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Explanation:
A proportional linear relationship is of the form y = kx
We can solve for k to get k = y/x.
Based on that, we can prove a table is a proportional linear relationship if and only if each column of x,y values divide to the same number.
Choice A shows that y/x = 2/8 = 1/4 for the first column; however, y/x = 8/16 = 1/2 for the second column. The outputs 1/4 and 1/2 not being the same indicates we don't have a constant k value for all of the columns. This is sufficient to show that table A is not a proportional linear relationship.
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In contrast, table B is a proportional linear relationship because we have these four divisions that lead to the same value (1/8)
- Column One: y/x = 2/16 = 1/8
- Column Two: y/x = 4/32 = 1/8
- Column Three: y/x = 6/48 = 1/8
- Column Four: y/x = 8/48 = 1/8
Showing that k = 1/8 for table B. The equation here is y = (1/8)x. We can rule out choice B.
I'll let you check out tables C and D on your own, but you should find that a similar situation shows up as did with table B. This indicates tables C and D are also proportional linear relationships. We can rule out choices C and D.
