The linear function given in the image is:

$f(x) = \frac{1}{4}x + 6$

This is in slope-intercept form, $f(x) = mx + b$, where:

• $m = \frac{1}{4}$ is the slope, which means the line rises 1 unit for every 4 units it runs to the right.
• $b = 6$ is the y-intercept, which means the line crosses the y-axis at $(0, 6)$.

To graph this:

1. Plot the y-intercept, $(0, 6)$.
2. Use the slope $\frac{1}{4}$ to find another point. From $(0, 6)$, move 4 units to the right and 1 unit up. This gives the point $(4, 7)$.
3. Draw a straight line through the points $(0, 6)$ and $(4, 7)$.

Would you like further details or have any other questions?

Here are some related questions:

1. How does the slope affect the steepness of the line?
2. What happens to the graph if the slope is negative?
3. How do you find the x-intercept of this function?
4. How does changing the y-intercept affect the graph's position?
5. Can you convert this equation into standard form?

Tip: The slope of a line can be interpreted as the rate of change of $y$ with respect to $x$.