1. **Problem Statement:** We are given points $P(-3,4)$ and $Q$ lies on the positive x-axis. We need to determine the gradient (slope) of the line segment $PQ$. 2. **Understanding the Gradient:** The gradient (or slope) of a line between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by the formula: $$\text{slope} = m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. **Identify Coordinates:** Point $P$ is $(-3,4)$. Since $Q$ lies on the positive x-axis, its $y$-coordinate is $0$. Let $Q = (x,0)$ where $x > 0$. 4. **Calculate the Gradient:** Using the formula, $$m = \frac{0 - 4}{x - (-3)} = \frac{-4}{x + 3}$$ 5. **Interpretation:** The gradient depends on the $x$-coordinate of $Q$. Without a specific $x$ value for $Q$, the gradient is expressed as a function of $x$: $$m = \frac{-4}{x + 3}$$ 6. **Summary:** The gradient of $PQ$ is $\frac{-4}{x + 3}$ where $Q = (x,0)$ and $x > 0$. If you provide the exact $x$-coordinate of $Q$, we can compute a numerical value for the gradient.