The equation you've provided is \( d = -0.5t + 7 \). This is a linear equation that can describe a relationship between two variables, \( d \) (dependent variable) and \( t \) (independent variable). Here's a breakdown:

### Key features of the equation:
1. **Slope**: The coefficient of \( t \) is \( -0.5 \), which is the slope. It indicates the rate of change of \( d \) with respect to \( t \). A slope of \( -0.5 \) means that for every 1 unit increase in \( t \), \( d \) decreases by 0.5 units.
   
2. **Intercept**: The constant \( 7 \) is the y-intercept. This is the value of \( d \) when \( t = 0 \). In this case, \( d = 7 \) when \( t = 0 \).

3. **Interpretation**: If this equation models a real-world scenario, such as distance over time or some other relationship, \( d \) decreases linearly as \( t \) increases.

### Example:
If \( t = 2 \):
\[
d = -0.5(2) + 7 = -1 + 7 = 6
\]
So, when \( t = 2 \), \( d = 6 \).

Would you like more details or have any questions?

Here are 5 related questions:
1. How would the graph of this equation look?
2. What happens to \( d \) as \( t \) increases?
3. How would you solve for \( t \) if \( d \) is given?
4. What real-life situations could this equation model?
5. How does changing the slope affect the equation?

**Tip**: The slope controls the steepness and direction of the line in a graph.

Explore how to solve and analyze the linear equation d = -0.5t + 7. Understand the slope-intercept form, the meaning of slope and y-intercept, and how the equation models a real-world scenario. Suitable for students in Grades 7-10.

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