The question is asking to sort the graphs of lines $l$ based on their gradients (slopes), from the smallest to the largest. There are five line graphs depicted.

Explanation of Gradients:

The gradient (slope) of a line is determined by how steep the line is and whether it is inclined positively or negatively:

• A horizontal line has a gradient of 0.
• A vertical line has an undefined gradient (which is the steepest possible).
• Positively sloped lines have positive gradients.
• Negatively sloped lines have negative gradients.

Analysis of the Lines:

Let's examine the slopes of each line:

1. The first graph shows a horizontal line, which has a gradient of 0.
2. The second graph shows a line sloping downward from left to right, indicating a negative gradient.
3. The third graph shows a vertical line, which has an undefined (very steep) gradient.
4. The fourth graph shows a line sloping upward from left to right, indicating a positive gradient.
5. The fifth graph is another negatively sloped line but steeper than the second graph, meaning its negative gradient is larger in magnitude.

Sorting the Lines:

1. Horizontal line (gradient = 0).
2. Steep negative line (larger negative gradient).
3. Shallow negative line (smaller negative gradient).
4. Shallow positive line (small positive gradient).
5. Vertical line (undefined, steepest possible gradient).

Thus, the order from smallest to largest gradient is:

$\text{(Negative Steep)} \rightarrow \text{(Negative Less Steep)} \rightarrow \text{(Horizontal, 0)} \rightarrow \text{(Positive)} \rightarrow \text{(Vertical, Undefined)}$

Do you need further details or clarifications?

Here are 5 related questions to further explore the concept:

1. How do you calculate the gradient of a line given two points on the line?
2. What happens to the slope of a line as it becomes more vertical?
3. How does the gradient relate to the angle the line makes with the x-axis?
4. What is the slope-intercept form of a linear equation?
5. How can you determine if two lines are perpendicular by comparing their slopes?

Tip: The steeper the line, the larger the absolute value of the gradient, with vertical lines having an undefined slope.