To graph the function \( f(z) = -\frac{5}{8}z + 87 \), we need to understand its form and key points. This is a linear equation of the form \( f(z) = mz + b \), where:

- \( m = -\frac{5}{8} \) is the slope.
- \( b = 87 \) is the y-intercept.

### Steps to Graph:
1. **Y-intercept**: Start by plotting the y-intercept at \( (0, 87) \).
2. **Slope**: The slope \( -\frac{5}{8} \) means that for every 8 units you move to the right (positive direction along the z-axis), you move down 5 units (negative direction along the y-axis). Conversely, moving 8 units to the left would move the graph 5 units up.
3. **Plot another point**: From the point \( (0, 87) \), move 8 units to the right and 5 units down, which gives the point \( (8, 82) \).
4. **Draw the line**: Connect these points and extend the line in both directions.

Would you like me to generate a graph for you? If yes, I can plot it for better visualization.

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### Related questions:
1. How would the graph change if the slope were positive?
2. What happens to the graph if we change the y-intercept to 100?
3. How do we find the x-intercept of the graph?
4. Can we determine if the function is increasing or decreasing based on the slope?
5. How does the graph relate to the concept of linearity?

### Tip:
When interpreting slopes, remember that negative slopes indicate a downward trend, while positive slopes indicate an upward trend.

Learn how to graph the linear equation f(z) = -5/8z + 87. This guide covers key concepts like slope-intercept form, identifying the slope and y-intercept, and plotting points. Suitable for students in Grades 8-10.

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