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The number line is a fundamental concept in mathematics used to represent numbers in a visual and linear way. It is particularly helpful when dealing with inequalities. To create a number line, draw a horizontal line and mark equal intervals along it, choosing a scale that suits the range of values you are dealing with. Each point on the line corresponds to a number, with values increasing as you move from left to right.

In the context of inequalities, the number line helps us visualize the set of possible solutions. With each point representing a possible value of the variable, it becomes easier to see which values satisfy the inequality. For the exercise given, we focus on the number '1', marking it clearly on our number line as a reference point for the inequality we are graphing.

Graphing inequalities on a number line involves different types of markers to show whether the endpoints are included as a part of the solution. When an inequality includes an 'equal to' part, such as with \( x \leq 1 \), we use a closed marker.

A closed marker is usually represented by a solid dot or circle, filled in to indicate that the number it marks is part of the solution. In our exercise, since we have \( x \leq 1 \), the number '1' is a solution to the inequality, and so a closed marker should be placed at '1' on the number line. This visually communicates to anyone reading the graph that if \( x \)=1, that value is included within the set of numbers that make the inequality true.

The phrase 'less than or equal to' is a crucial component of our inequality and affects how we graph it on the number line. For \( x \leq 1 \), this means that \( x \) is any number that is either less than '1' or exactly equal to '1'. As such, every number to the left of '1' on our number line is a part of the solution.

To graph this, from the point marked '1' with a closed marker, we draw an arrow stretching to the left. This arrow extends indefinitely, showcasing that all numbers less than '1' are solutions to the inequality. The inclusion of '1' itself in the solution set is already indicated by the closed marker. This graphical representation on a number line provides an immediate visual understanding of the range of values that satisfy the inequality \( x \leq 1 \).