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.