The image asks to find the gradient (or slope) of the line segment joining each pair of points.

To find the gradient (slope) $m$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$, use the formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Let's calculate the slope for each pair of points listed:

a) Points $(3, 1)$ and $(5, 5)$

$m = \frac{5 - 1}{5 - 3} = \frac{4}{2} = 2$

b) Points $(4, 7)$ and $(10, 9)$

$m = \frac{9 - 7}{10 - 4} = \frac{2}{6} = \frac{1}{3}$

c) Points $(6, 1)$ and $(2, 5)$

$m = \frac{5 - 1}{2 - 6} = \frac{4}{-4} = -1$

d) Points not fully visible in image

For part d), the image cuts off the full set of coordinates. If you provide the missing points, I can calculate that slope as well.

Would you like more details or have any further questions? Here are some related questions:

1. What is the significance of the gradient in a real-world context?
2. How does a vertical line’s slope differ from a horizontal line’s slope?
3. What happens if two points lie on the same vertical line?
4. How would you find the equation of a line if you are given two points?
5. Can the slope of a line change between two fixed points?

Tip: Remember, if the denominator in the slope formula is zero, the line is vertical and the slope is undefined.