To determine which graph shows the graph of a linear function with an initial value of $-5$, the initial value refers to the y-intercept of the function. This is the point where the line crosses the y-axis.

Observations from the graphs:

• Graph A: The line crosses the y-axis at $y = -5$.
• Graph B: The line crosses the y-axis at $y = 0$.
• Graph C: The line crosses the y-axis at $y = 5$.
• Graph D: The line crosses the y-axis at $y = 3$.

Conclusion:

The correct graph is A, as it shows the y-intercept (initial value) of $-5$.

Let me know if you need a detailed explanation or further assistance.

Expanding with Related Questions:

1. How can you determine the slope of a line from a graph?
2. What does the slope represent in a linear function?
3. How would the graph change if the initial value was changed to $5$?
4. How do you derive the equation of a line given its graph?
5. Can you identify whether a linear graph has a positive or negative slope just by looking?

Tip: Always focus on the point where the line crosses the y-axis when identifying the y-intercept of a graph!