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).