To find the x-intercept of a line, you need to determine the point where the line crosses the x-axis. At this point, the y-coordinate is 0.

We already derived the equation of line $DE$ from part b(ii). Let's go through the steps again to find the x-intercept clearly.

Steps:

1. Find the slope of $DE$:

   • We previously calculated the slope of $DE$ as $\frac{7}{12}$.

2. Find the equation of line $DE$:

   • Using the point-slope form of the equation of a line: $y - y_1 = m(x - x_1)$ where $m$ is the slope, and $(x_1, y_1)$ is a point on the line.

   • Let's use point $D(-4, 2)$ and the slope $m = \frac{7}{12}$ to write the equation of line $DE$: $y - 2 = \frac{7}{12}(x - (-4)) = \frac{7}{12}(x + 4)$ Simplifying: $y - 2 = \frac{7}{12}x + \frac{7 \times 4}{12} = \frac{7}{12}x + \frac{28}{12} = \frac{7}{12}x + \frac{7}{3}$ So the equation of line $DE$ is: $y = \frac{7}{12}x + \frac{7}{3} + 2 = \frac{7}{12}x + \frac{13}{3}$

3. **Set ( y =