To find the x-intercept of the line, we set $y = 0$ in the equation $9x - 3y = 24$, since the x-intercept is where the line crosses the x-axis (where $y = 0$).

Starting with the equation:

$9x - 3y = 24$

Substitute $y = 0$:

$9x - 3(0) = 24$

$9x = 24$

Now, solve for $x$:

$x = \frac{24}{9} = \frac{8}{3}$

Thus, the x-intercept is $\left( \frac{8}{3}, 0 \right)$.

Would you like a deeper explanation of how this process works, or any other details?

Here are 5 related questions for further practice:

1. Find the y-intercept of the line $9x - 3y = 24$.
2. What is the slope of the line $9x - 3y = 24$?
3. Write the equation of the line $9x - 3y = 24$ in slope-intercept form.
4. Find the x-intercept of the line $7x + 2y = 14$.
5. Determine the intercepts of the line $5x - 4y = 20$.

Tip: The x-intercept occurs when $y = 0$, and the y-intercept occurs when $x = 0$.