We are given the linear function $f(x) = \frac{1}{2}x - 1$. To graph this, we will use the slope-intercept form of a line, which is:

$y = mx + b$

Here:

• $m$ is the slope.
• $b$ is the y-intercept.

From the equation $f(x) = \frac{1}{2}x - 1$, we can identify:

• The slope $m = \frac{1}{2}$, meaning the line rises by 1 unit for every 2 units it moves to the right.
• The y-intercept $b = -1$, meaning the line crosses the y-axis at $(0, -1)$.

Steps to graph the function:

1. Plot the y-intercept: Start at the point $(0, -1)$ on the y-axis.
2. Use the slope $\frac{1}{2}$: From $(0, -1)$, move up 1 unit and 2 units to the right to get the second point $(2, 0)$.
3. Draw the line: Connect the points and extend the line in both directions.

Would you like me to create a graph for you, or do you have any questions?

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Here are 5 follow-up questions related to the topic:

1. What is the significance of the slope in a linear equation?
2. How does changing the slope affect the steepness of the graph?
3. What happens if the y-intercept changes but the slope remains the same?
4. How can we determine the x-intercept from this equation?
5. How would the graph look if the slope was negative?

Tip: Always check both the slope and y-intercept before drawing a graph to ensure accuracy.