Find the gradient of a line with point A (-2,4), B(-6,8)

To find the gradient (slope) of a line passing through two points, we use the formula:

\[
\text{Gradient (m)} = \frac{y_2 - y_1}{x_2 - x_1}
\]

Here, the coordinates of point \( A \) are \( (-2, 4) \) and the coordinates of point \( B \) are \( (-6, 8) \).

Substituting these values into the formula:

\[
m = \frac{8 - 4}{-6 - (-2)} = \frac{4}{-6 + 2} = \frac{4}{-4} = -1
\]

So, the gradient of the line is \( -1 \).

Would you like a detailed explanation, or do you have any further questions?

Here are 5 related questions:
1. How do you find the equation of the line using this gradient and one of the points?
2. What is the significance of a negative gradient?
3. How do you interpret the gradient when it's zero or undefined?
4. How would the gradient change if you swapped the points \( A \) and \( B \)?
5. Can you calculate the midpoint of the line segment joining points \( A \) and \( B \)?

**Tip:** Always check the signs when subtracting the coordinates to avoid calculation errors.

Learn how to find the gradient (slope) of a line passing through the points A (-2, 4) and B (-6, 8) using the slope formula. This problem covers fundamental coordinate geometry concepts, including linear equations, and is suitable for students in Grades 6-8.

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