The gradient (or slope) of a line passing through two points $A(x_1, y_1)$ and $B(x_2, y_2)$ is given by the formula:

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

Given points:

• $A(1, 4)$ where $x_1 = 1$ and $y_1 = 4$
• $B(3, 10)$ where $x_2 = 3$ and $y_2 = 10$

Substituting the values into the formula:

$\text{Gradient} = \frac{10 - 4}{3 - 1} = \frac{6}{2} = 3$

So, the gradient of the line is 3.

Orientation of the line:

The orientation of a line refers to the direction in which it slopes. Since the gradient is positive (3), the line has an upward slope as we move from left to right. This means the line is ascending.

Summary:

• The gradient of the line is 3.
• The orientation of the line is upward (ascending) from left to right.

Would you like further details on how to calculate the equation of this line, or any other related concepts?

Here are some follow-up questions to explore:

1. How would you calculate the equation of a line given two points?
2. What happens to the orientation of a line if the gradient is negative?
3. How can the gradient be used to determine if two lines are parallel or perpendicular?
4. What does it mean when the gradient of a line is zero?
5. How can you find the gradient of a vertical line?

Tip: A positive gradient indicates an ascending line (rising from left to right), and a negative gradient indicates a descending line (falling from left to right).