. Given the equation y = 5 - 0.4x, identify if it represents growth or decay, if it is linear or exponential, and what the initial amount is.

Given the equation \( y = 5 - 0.4x \), let's analyze its characteristics:

1. **Linear or Exponential**:  
   The equation is in the form \( y = mx + c \), which is a linear equation. Therefore, it represents a **linear** relationship.

2. **Growth or Decay**:  
   The coefficient of \( x \) is \(-0.4\), which is negative. This means that as \( x \) increases, \( y \) decreases. Therefore, this equation represents **decay**.

3. **Initial Amount**:  
   The initial amount is the value of \( y \) when \( x = 0 \). Plugging in \( x = 0 \):
   \[
   y = 5 - 0.4(0) = 5
   \]
   So, the initial amount is **5**.

### Summary:
- **Linear** equation
- Represents **decay**
- **Initial amount**: 5

Would you like further details or have any questions? Here are some related questions:

1. What does the slope of the equation represent?
2. How would the graph of this equation look?
3. What would the equation represent if the coefficient of \( x \) was positive?
4. How do you find the x-intercept for this equation?
5. How would you rewrite this equation if it represented growth?
6. What is the rate of decay in this equation?
7. How does the initial amount affect the graph?
8. How would the equation change if the initial amount was different?

**Tip**: In a linear equation, the slope determines the rate of increase or decrease, while the y-intercept gives the starting value of \( y \).

Understand the characteristics of the linear equation y = 5 - 0.4x, including whether it represents growth or decay, its linearity, and the initial amount. Explore how the coefficient affects the trend of y with changes in x. Suitable for students in Grades 7-9.

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