Question

In a certain​ neighborhood, the front side of each house has 7 windows. Complete the table. Describe the relationship between the number of houses and the total number of front windows. Then use the table to graph the relationship.

Answer 1

To analyze the relationship between the number of houses and the total number of front windows, we will showcase a simple mathematical relationship. Given that each house has 7 windows, we can derive the total number of windows based on the number of houses.

Let's create a table with a few example values:

| Number of Houses | Total Number of Windows |
|------------------|------------------------|
| 1 | 7 |
| 2 | 14 |
| 3 | 21 |
| 4 | 28 |
| 5 | 35 |
| 6 | 42 |
| 7 | 49 |
| 8 | 56 |
| 9 | 63 |
| 10 | 70 |

### Relationship Description

The relationship between the number of houses (let's denote it as \( H \)) and the total number of front windows (denote as \( W \)) can be expressed with a simple linear equation:

\[ W = 7H \]

This means the total number of windows is directly proportional to the number of houses. As the number of houses increases, the total number of front windows increases linearly.

### Graphing the Relationship

To graph this relationship, you can plot the number of houses on the x-axis and the total number of windows on the y-axis.

1. The x-axis will range from 0 to a little over 10 (since we have data for 10 houses).
2. The y-axis will range from 0 to at least 70 (since the maximum total number of windows from the table is 70).
3. Each point on the graph will represent the number of houses and the corresponding total number of windows.

The line formed by connecting these points will be straight, indicating a linear relationship.

You can graph it using graph paper, or utilize software tools to create a line graph based on the data points provided in the table. The slope of the line will be 7, which is the number of windows per house.