Question

Either Table C or Table D shows a proportional relationship.



Plot all the points from the table that shows a proportional relationship.

Keyboard Instructions
Initial graph state
The horizontal axis goes from -1 to 11 with ticks spaced every 1 unit(s).
The vertical axis goes from -1 to 11 with ticks spaced every 1 unit(s).


Table C

x 2 4 6 8
y 1 3 5 7


Table D

x 2 6 8 10
y 1 3 4 5

Answer 1

To determine which table shows a proportional relationship, we need to check if the ratio \( \frac{y}{x} \) is constant for all points in each table.

### Table C

- For \( x = 2, y = 1 \):
\[
\frac{y}{x} = \frac{1}{2} = 0.5
\]
- For \( x = 4, y = 3 \):
\[
\frac{y}{x} = \frac{3}{4} = 0.75
\]
- For \( x = 6, y = 5 \):
\[
\frac{y}{x} = \frac{5}{6} \approx 0.833
\]
- For \( x = 8, y = 7 \):
\[
\frac{y}{x} = \frac{7}{8} = 0.875
\]

Since the ratios are not constant, Table C does not represent a proportional relationship.

### Table D

- For \( x = 2, y = 1 \):
\[
\frac{y}{x} = \frac{1}{2} = 0.5
\]
- For \( x = 6, y = 3 \):
\[
\frac{y}{x} = \frac{3}{6} = 0.5
\]
- For \( x = 8, y = 4 \):
\[
\frac{y}{x} = \frac{4}{8} = 0.5
\]
- For \( x = 10, y = 5 \):
\[
\frac{y}{x} = \frac{5}{10} = 0.5
\]

Since the ratios are constant and equal to \( 0.5 \), Table D does represent a proportional relationship.

### Plotting the points from Table D

The points from Table D are:
- (2, 1)
- (6, 3)
- (8, 4)
- (10, 5)

To plot these points on the coordinate plane:

1. Plot point (2, 1).
2. Plot point (6, 3).
3. Plot point (8, 4).
4. Plot point (10, 5).

These points can be marked on the graph accordingly!