hint:%20the%20constant%20of%20proportionality%20means%20you%20are%20solving%20for%20how%20many%20%22y's%22%20there%20are%20for%20each%20%22x%22.%20Set%20up%20your%20equation%20as%20%22(y)/(x)%22%20to%20find%20the%20constant%20of%20proportionality.%20Check%20each%20set%20of%20numbers%20on%20your%20table%20before%20selecting%20your%20answer.%C2%A0%0A*%0A10%20points%0A%0A1/4%0A4%0A1/8%0A8 What is the answer?

Answer 1

To find the constant of proportionality, you can set up the equation \( \frac{y}{x} \). The constant of proportionality is the value you get when you divide \( y \) by \( x \) for each pair of numbers in your table.

Let's calculate \( \frac{y}{x} \) for each of the given pairs:

1. For \( \frac{1}{4} \):

   • If \( x = 1 \) and \( y = 4 \): \( \frac{y}{x} = \frac{4}{1} = 4 \)

2. For \( \frac{4}{1} \):

   • If \( x = 4 \) and \( y = 1 \): \( \frac{y}{x} = \frac{1}{4} = 0.25 \)

3. For \( \frac{1}{8} \):

   • If \( x = 1 \) and \( y = 8 \): \( \frac{y}{x} = \frac{8}{1} = 8 \)

4. For \( 8 \):

   • If \( x = 8 \) and \( y = 1 \): \( \frac{y}{x} = \frac{1}{8} = 0.125 \)

Now, to find if any of these pairs share a constant of proportionality, we identify the ratio:

• \( \frac{4}{1} = 4 \)
• \( \frac{1}{4} = 0.25 \)
• \( \frac{8}{1} = 8 \)
• \( \frac{1}{8} = 0.125 \)

None of the ratios are equal; thus, there's no single constant of proportionality among the presented pairs. Therefore, to select an answer, please clarify if you're looking for the calculation for a specific context or a choice of answer based on proportional relationships.