Question

The Fox Valley Middle School's colors are purple and white. Heather enjoys making flags for her classmates to wave at school sporting events. She makes 7 purple flags for every 2 white flags.
Complete the table.
Purple flags 7 35
White flags 2 4 6
Graph the data from the table.

Answer 1

To complete the table and find the number of white flags corresponding to the given purple flags, we can establish a relationship based on the ratio of purple to white flags. Heather makes 7 purple flags for every 2 white flags, so the ratio of purple to white flags is 7:2.

To fill in the table, we can express the counts of flags as multiples of the basic ratio:

1. **For the existing data:**
- When there are 7 purple flags, there are 2 white flags.
- When there are 35 purple flags:
Using the ratio (7 purple : 2 white),
We can set up a proportion:
\[
\frac{7}{2} = \frac{35}{x}
\]
Cross-multiplying gives:
\[
7x = 70 \quad \Rightarrow \quad x = 10
\]
So there are 10 white flags corresponding to 35 purple flags.

Now we can fill in the table with values:

| Purple flags | 7 | 14 | 21 | 28 | 35 |
|--------------|---|----|----|----|----|
| White flags | 2 | 4 | 6 | 8 | 10 |

### Graphing the Data

To graph the data from the table, set up a coordinate system:

- **X-axis:** Number of Purple Flags
- **Y-axis:** Number of White Flags

Plot the following points based on the completed table:
- (7, 2)
- (14, 4)
- (21, 6)
- (28, 8)
- (35, 10)

### Graph Details:
- Mark each point on the graph accordingly.
- Connect the points with a line if you wish to show the continuous nature of the ratio.

The graph will show a straight line, indicating a constant ratio between the number of purple flags and white flags as Heather makes them.