To find the $x$-intercept of the function $f(x) = \frac{1}{5}x - 6$, we set $f(x) = 0$, because the $x$-intercept occurs where the function crosses the $x$-axis, and at that point, $y = 0$.

Steps:

1. Set $f(x) = 0$: $0 = \frac{1}{5}x - 6$

2. Solve for $x$: $\frac{1}{5}x = 6$ Multiply both sides by 5: $x = 30$

3. The $x$-intercept is $(30, 0)$.

Final Answer:

The $x$-intercept is: $(30, 0)$

Do you have any questions or would you like further explanation?

Here are 5 related questions to deepen your understanding:

1. How do you find the $y$-intercept of a linear function?
2. What is the slope of the line $f(x) = \frac{1}{5}x - 6$?
3. How would the graph of $f(x) = \frac{1}{5}x - 6$ change if the slope were negative?
4. How do you verify if a point lies on the line $f(x) = \frac{1}{5}x - 6$?
5. What is the geometric significance of the $x$-intercept in a real-world context?

Tip: When solving for intercepts, remember that the $x$-intercept occurs when $y = 0$, and the $y$-intercept occurs when $x = 0$.