1. **State the problem:** We are given two functions $f(x) = \frac{1}{4}x - 9$ and $g(x) = \frac{3}{4}x + 21$. The function $h$ is defined as $h(x) = f(x) + g(x)$. We need to find the $x$-coordinate of the $x$-intercept of the graph of $y = h(x)$. 2. **Write the formula for $h(x)$:** Since $h(x) = f(x) + g(x)$, substitute the expressions: $$h(x) = \left(\frac{1}{4}x - 9\right) + \left(\frac{3}{4}x + 21\right)$$ 3. **Simplify $h(x)$:** Combine like terms: $$h(x) = \frac{1}{4}x + \frac{3}{4}x - 9 + 21 = \left(\frac{1}{4} + \frac{3}{4}\right)x + 12 = 1x + 12 = x + 12$$ 4. **Find the $x$-intercept:** The $x$-intercept occurs where $y = h(x) = 0$: $$0 = x + 12$$ Solve for $x$: $$x = -12$$ 5. **Interpretation:** The graph of $y = h(x)$ crosses the $x$-axis at $x = -12$. **Final answer:** The $x$-coordinate of the $x$-intercept is $\boxed{-12}$.