To find the gradient (or slope) of side \( BC \), we use the formula for the slope between two points \( (x_1, y_1) \) and \( (x_2, y_2) \):
\[
\text{slope} = m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Here, the coordinates of points \( B \) and \( C \) are:
- \( B(-7, -6) \)
- \( C(7, 4) \)

### Step 1: Apply the slope formula
Substitute the coordinates of \( B \) and \( C \) into the slope formula:
\[
m = \frac{4 - (-6)}{7 - (-7)} = \frac{4 + 6}{7 + 7} = \frac{10}{14} = \frac{5}{7}
\]

### Final Answer
The gradient (slope) of side \( BC \) is \( \frac{5}{7} \).

Would you like any further explanation on the slope calculation, or do you have any other questions?

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Here are some related questions:
1. How does the slope \( \frac{5}{7} \) indicate the direction of side \( BC \)?
2. What would the slope of side \( AB \) be, given points \( A \) and \( B \)?
3. How would the slope change if we reflected the triangle across the y-axis?
4. Can you find the equation of the line that passes through points \( B \) and \( C \)?
5. How does the slope of side \( BC \) compare to the slope of side \( AC \)?

Tip: The slope provides a quick understanding of the steepness and direction of a line.

Learn how to find the gradient (slope) of side BC using the slope formula. This problem involves calculating the slope between points B(-7, -6) and C(7, 4). Understand the direction and steepness of side BC in this analytic geometry problem. Suitable for high school students studying analytic geometry.

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