The problem asks to graph the linear function $f(x) = \frac{1}{4}x + 7$. Let me guide you on how to graph this step by step:

Steps to Graph $f(x) = \frac{1}{4}x + 7$:

1. Identify the slope ($m$) and y-intercept ($b$):

   • The equation is in slope-intercept form $y = mx + b$, where:
     • $m = \frac{1}{4}$ (slope)
     • $b = 7$ (y-intercept).

2. Plot the y-intercept:

   • The y-intercept is where $x = 0$. Plot the point $(0, 7)$ on the graph.

3. Use the slope to find another point:

   • Slope $m = \frac{1}{4}$ means that for every increase of 4 units in $x$, $y$ increases by 1 unit.
   • Starting from $(0, 7)$, move 4 units to the right and 1 unit up to get the second point $(4, 8)$.

4. Draw the line:

   • Use a ruler to draw a straight line through the points $(0, 7)$ and $(4, 8)$. Extend it in both directions.

Would you like me to generate a visual graph of this function? Let me know if you need more details!

Here are 5 questions to further understand the concept:

1. How does the slope $\frac{1}{4}$ influence the steepness of the line?
2. What happens to the graph if the y-intercept changes from 7 to another number?
3. How would you graph this equation if the slope was negative?
4. Why is it important to plot at least two points when drawing a line?
5. What real-life situations can be modeled using linear equations like this one?

Tip: Always double-check your plotted points to ensure they align with the slope!