Question

Which of the following tables represents a proportional relationship?
Table A.
x 4 6 8 10
y 6 9 12 15


Table B.
x 1 4 7 10
y 0 3 6 9


Table C.
x 2 4 6 8
y 3 4 5 6


Table D.
x 2 3 4 5
y 3 6 9 12

Answer 1

** ISNT AN OPTION

Answer 2

To determine which table represents a proportional relationship, we need to check if the ratio \( \frac{y}{x} \) is constant for all corresponding pairs of \( x \) and \( y \).

**Table A:**
- \( \frac{6}{4} = 1.5 \)
- \( \frac{9}{6} = 1.5 \)
- \( \frac{12}{8} = 1.5 \)
- \( \frac{15}{10} = 1.5 \)

Since the ratio is constant (1.5), Table A represents a proportional relationship.

**Table B:**
- \( \frac{0}{1} = 0 \)
- \( \frac{3}{4} = 0.75 \)
- \( \frac{6}{7} \approx 0.857 \)
- \( \frac{9}{10} = 0.9 \)

The ratios are not constant, so Table B does not represent a proportional relationship.

**Table C:**
- \( \frac{3}{2} = 1.5 \)
- \( \frac{4}{4} = 1 \)
- \( \frac{5}{6} \approx 0.833 \)
- \( \frac{6}{8} = 0.75 \)

The ratios are not constant, so Table C does not represent a proportional relationship.

**Table D:**
- \( \frac{3}{2} = 1.5 \)
- \( \frac{6}{3} = 2 \)
- \( \frac{9}{4} = 2.25 \)
- \( \frac{12}{5} = 2.4 \)

The ratios are not constant, so Table D does not represent a proportional relationship.

Thus, only **Table A** represents a proportional relationship.

Answer 3

Apologies for the oversight in my response. Let’s reevaluate the tables carefully to find which one represents a proportional relationship.

A relationship is proportional if the ratio \( \frac{y}{x} \) is constant for all pairs of \( (x, y) \).

**Table A:**
- \( x = 4, y = 6: \frac{y}{x} = \frac{6}{4} = 1.5 \)
- \( x = 6, y = 9: \frac{y}{x} = \frac{9}{6} = 1.5 \)
- \( x = 8, y = 12: \frac{y}{x} = \frac{12}{8} = 1.5 \)
- \( x = 10, y = 15: \frac{y}{x} = \frac{15}{10} = 1.5 \)

The ratio is constant at \( 1.5 \), so Table A represents a proportional relationship.

**Table B:**
- \( x = 1, y = 0: \frac{y}{x} = \frac{0}{1} = 0 \)
- \( x = 4, y = 3: \frac{y}{x} = \frac{3}{4} = 0.75 \)
- \( x = 7, y = 6: \frac{y}{x} = \frac{6}{7} \approx 0.857 \)
- \( x = 10, y = 9: \frac{y}{x} = \frac{9}{10} = 0.9 \)

The ratios are not constant, so Table B does not represent a proportional relationship.

**Table C:**
- \( x = 2, y = 3: \frac{y}{x} = \frac{3}{2} = 1.5 \)
- \( x = 4, y = 4: \frac{y}{x} = \frac{4}{4} = 1 \)
- \( x = 6, y = 5: \frac{y}{x} = \frac{5}{6} \approx 0.833 \)
- \( x = 8, y = 6: \frac{y}{x} = \frac{6}{8} = 0.75 \)

The ratios are not constant, so Table C does not represent a proportional relationship.

**Table D:**
- \( x = 2, y = 3: \frac{y}{x} = \frac{3}{2} = 1.5 \)
- \( x = 3, y = 6: \frac{y}{x} = \frac{6}{3} = 2 \)
- \( x = 4, y = 9: \frac{y}{x} = \frac{9}{4} = 2.25 \)
- \( x = 5, y = 12: \frac{y}{x} = \frac{12}{5} = 2.4 \)

The ratios are not constant, so Table D does not represent a proportional relationship.

After reviewing again, **Table A** does represent a proportional relationship. If you are looking for a different conclusion, please clarify or provide additional context regarding the options and requirements!