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To determine the gradient (or slope) of the line \( AB \), you can use the formula for the slope between two points \( A(x_1, y_1) \) and \( B(x_2, y_2) \):

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

Given the points \( A(2, 1) \) and \( B(-4, -3) \):

- \( x_1 = 2 \), \( y_1 = 1 \)
- \( x_2 = -4 \), \( y_2 = -3 \)

Now, plug in the values:

\[
m = \frac{-3 - 1}{-4 - 2} = \frac{-4}{-6} = \frac{2}{3}
\]

So, the gradient of \( AB \) is \( \frac{2}{3} \).

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you find the length of a line segment between two points?
2. What is the significance of the slope in a linear equation?
3. How can you determine if two lines are parallel or perpendicular using their slopes?
4. What is the equation of the line passing through points \( A(2, 1) \) and \( B(-4, -3) \)?
5. How would you find the area of triangle \( ABC \) using the given coordinates?

**Tip:** Remember that the slope of a line indicates the direction and steepness of the line. A positive slope means the line ascends from left to right, while a negative slope means it descends.

Learn how to determine the gradient (slope) of line AB using analytical geometry principles. Given points A(2, 1) and B(-4, -3), calculate the slope step-by-step with the formula: slope = (y2 - y1) / (x2 - x1). Suitable for students in Grades 7-9.

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