Each Friday, the school prints 400 copies of the school newsletter. The equation c = 400w models the relationship between the number of weeks and the total number of copies of the newsletters printed. What is true of the graph of this scenario?



A viable point on the graph is
.

The values of w must be

1 answer

Let's analyze the given equation and the statements to understand what is true about the graph.

The equation provided is:
\[ c = 400w \]

Here, \( c \) represents the total number of copies of the newsletters printed, and \( w \) represents the number of weeks.

### Slope and Intercept

This equation is in the form of a linear equation \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. In this specific equation:
- The slope \( m \) is 400. This means that for each additional week, the number of newsletters printed increases by 400.
- The y-intercept \( b \) is 0. This means that at week 0, the total number of copies printed is 0.

### Viable Points

A viable point on the graph (w, c) would be one that satisfies the equation \( c = 400w \) with non-negative integer values of \( w \) (since negative weeks and non-integer weeks aren't practical in this context).

For example:
- When \( w = 1 \), \( c = 400 \times 1 = 400 \). So, (1, 400) is a point on the graph.
- When \( w = 2 \), \( c = 400 \times 2 = 800 \). So, (2, 800) is a point on the graph.
- When \( w = 3 \), \( c = 400 \times 3 = 1200 \). So, (3, 1200) is a point on the graph.

### Values of \( w \)

Since \( w \) represents the number of weeks, it must be a non-negative integer. Specifically:
\[ w \geq 0 \]
This means \( w \) can be any whole number (0, 1, 2, 3, etc.).

### Conclusion

Given the analysis:
1. A viable point on the graph could be any point corresponding to a non-negative integer \( w \) and its respective \( c \) value. For example, (1, 400), (2, 800), etc.
2. The values of \( w \) must be non-negative integers, i.e., \( w \geq 0 \).

### Correct Responses

- **A viable point on the graph:** (1, 400), (2, 800), (3, 1200), ...
- **The values of \( w \) must be:** Non-negative integers ( \( w \geq 0 \) )