To find the gradient (slope) of the line segment \(BC\) in triangle \(ABC\), we will use the coordinates of points \(B\) and \(C\). 

### Given:
- \(B(-7, -6)\)
- \(C(9, 2)\)

### Formula for Gradient:
The gradient (slope) \(m\) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

### Apply the Formula:

For points \(B(-7, -6)\) and \(C(9, 2)\):

\[
m_{BC} = \frac{2 - (-6)}{9 - (-7)}
\]

Simplify the expression:

\[
m_{BC} = \frac{2 + 6}{9 + 7}
\]
\[
m_{BC} = \frac{8}{16}
\]
\[
m_{BC} = \frac{1}{2}
\]

### Conclusion:
The gradient of line segment \(BC\) is \(\frac{1}{2}\).

Would you like more details on this, or do you have any other questions?

### Related Questions:
1. How do you find the equation of line \(BC\) using its gradient and a point?
2. What is the perpendicular gradient to line \(BC\)?
3. How can you find the distance between points \(B\) and \(C\)?
4. How would the gradient change if the coordinates of point \(B\) or \(C\) were different?
5. How do you determine if two lines are parallel using their gradients?

### Tip:
When calculating the gradient of a line, remember that a positive gradient indicates an increasing slope (uphill), and a negative gradient indicates a decreasing slope (downhill).

Learn how to find the gradient (slope) of the line segment BC in triangle ABC using coordinate geometry. This problem involves calculating the gradient between two points, B(-7, -6) and C(9, 2). Suitable for high school students.

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