To find the gradient (slope) between two points $(x_1, y_1)$ and $(x_2, y_2)$, we use the formula:

$\text{Gradient} = \frac{y_2 - y_1}{x_2 - x_1}$

Let's solve for each pair of points in the image:

1. For $A(0, -4)$ and $B(4, 4)$: $\text{Gradient} = \frac{4 - (-4)}{4 - 0} = \frac{4 + 4}{4} = \frac{8}{4} = 2$

2. For $C(0, 0)$ and $D(2, -4)$: $\text{Gradient} = \frac{-4 - 0}{2 - 0} = \frac{-4}{2} = -2$

3. For $M(-4, 0)$ and $N(-2, 4)$: $\text{Gradient} = \frac{4 - 0}{-2 - (-4)} = \frac{4 - 0}{-2 + 4} = \frac{4}{2} = 2$

4. For $X(-6, -2)$ and $Y(-3, -5)$: $\text{Gradient} = \frac{-5 - (-2)}{-3 - (-6)} = \frac{-5 + 2}{-3 + 6} = \frac{-3}{3} = -1$

Final gradients:

1. $A$ and $B$: 2
2. $C$ and $D$: -2
3. $M$ and $N$: 2
4. $X$ and $Y$: -1

Would you like more details on any of these calculations?

Follow-up questions:

1. What is the meaning of a positive gradient?
2. What happens if the gradient is zero?
3. How would you find the equation of a line given two points?
4. Can two different pairs of points have the same gradient?
5. What is the relationship between gradients and parallel lines?

Tip: When calculating gradients, always subtract coordinates consistently to avoid mistakes.