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To determine the gradient (or slope) of line BC, we use the gradient formula for two points \((x_1, y_1)\) and \((x_2, y_2)\):

\[
\text{Gradient of BC} = \frac{y_2 - y_1}{x_2 - x_1}
\]

In this case, the coordinates of \(B\) are \((-8, 2)\) and the coordinates of \(C\) are \((4, 6)\).

Now, let's substitute these values into the formula:

\[
\text{Gradient of BC} = \frac{6 - 2}{4 - (-8)} = \frac{4}{4 + 8} = \frac{4}{12} = \frac{1}{3}
\]

Thus, the gradient of line BC is \(\frac{1}{3}\).

Would you like further details or have any questions?

Here are five related questions to deepen understanding:
1. How would you find the equation of the line BC using the gradient and a point?
2. How does the gradient of AD compare to BC?
3. How do you calculate the midpoint of BC?
4. What does the gradient tell you about the orientation of the line?
5. Can the gradient be used to determine perpendicularity or parallelism between lines?

**Tip**: The gradient helps determine how steep a line is; the larger the gradient, the steeper the line.

This guide explains how to find the gradient of line segment BC in triangle ABC with vertices A(-3,7), B(-8,2), and C(4,6). It uses the gradient formula to show step-by-step calculations, suitable for students in Grades 9-10.

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