To understand the relationship between the number of weeks (w) and the total number of copies (c) as described by the equation [tex]\( c = 400w \)[/tex], let's analyze and break down the components of the equation and their implications.
### Step-by-Step Analysis
1. Identify the equation and variables:
- The equation provided is [tex]\( c = 400w \)[/tex].
- Here, [tex]\( c \)[/tex] represents the total number of copies of the newsletter.
- [tex]\( w \)[/tex] represents the number of weeks.
2. Understanding the relationship:
- The equation [tex]\( c = 400w \)[/tex] tells us that each week, 400 copies of the newsletter are printed.
- Therefore, if [tex]\( w = 1 \)[/tex] (one week), then [tex]\( c = 400 \times 1 = 400 \)[/tex] copies.
- This relationship is linear, meaning as the number of weeks increases, the total number of copies increases proportionally.
3. Determine a viable point:
- For a particular example, let’s take [tex]\( w = 1 \)[/tex], which is one week.
- Substituting [tex]\( w = 1 \)[/tex] into the equation, we get:
[tex]\[
c = 400 \times 1 = 400
\][/tex]
- Therefore, a viable point (a specific point that lies on the graph of this equation) would be [tex]\((w, c) = (1, 400)\)[/tex].
4. Conditions for [tex]\( w \)[/tex]:
- [tex]\( w \)[/tex] represents the number of weeks.
- Since the number of weeks cannot be negative or fractional, [tex]\( w \)[/tex] must be a non-negative integer (i.e., 0, 1, 2, 3, ...).
### Conclusion
Based on the analysis, the answers to the questions about the graph of this scenario are:
1. A viable point on the graph is:
[tex]\[
(1, 400)
\][/tex]
2. The values of [tex]\( w \)[/tex] must be:
[tex]\[
w \text{ must be a non-negative integer}
\][/tex]
Thus, these answers convey the behavior and constraints of the given linear relationship between the number of weeks and the total number of newsletters printed.
