The function you've provided is:

\[
f(x) = \frac{1}{2}x + 1
\]

This is a linear function of the form \(f(x) = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

- The slope (\(m\)) is \( \frac{1}{2} \). This means that for every increase of 1 in \(x\), the value of \(f(x)\) increases by \( \frac{1}{2} \).
- The y-intercept (\(b\)) is 1, meaning the graph of this function crosses the y-axis at \( (0, 1) \).

### Graphing Details:
1. The line will slope upwards because the slope is positive (\( \frac{1}{2} \)).
2. The point \( (0, 1) \) is where the line crosses the y-axis.
3. Another point on the line can be found by substituting a value for \(x\). For example:
   - If \(x = 2\), then \(f(2) = \frac{1}{2}(2) + 1 = 1 + 1 = 2\). So the point \( (2, 2) \) is also on the line.

Would you like further details on how to plot this or explore other aspects?

### Follow-up questions:
1. How would the graph change if the slope were negative?
2. What is the significance of the y-intercept in real-world scenarios?
3. Can you find the x-intercept for this function?
4. How do you calculate the slope between two points on this line?
5. What happens to the graph if we change the equation to \(f(x) = \frac{1}{2}x - 1\)?

**Tip:** The slope of a linear equation describes how steep the line is.

Explore the linear function f(x) = 1/2x + 1, which covers key algebra concepts such as slope and y-intercept. Learn how to graph the function, identify important points, and understand how changes in slope and intercept affect the graph. Suitable for students in Grades 6-8.

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