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.