what does n less than or equal to graph line example

Answer 1

It seems you're asking about the representation of the inequality "n less than or equal to" on a graph line, presumably a number line or possibly a Cartesian coordinate system. Let's start with the most common example, the number line.

If you have an inequality such as "n ≤ 5" (which reads as "n is less than or equal to 5"), you would represent this on a number line in the following way:

1. Draw a horizontal line and mark points at regular intervals, assigning them values as you would on a typical number line. Make sure that the number 5 is included among the values on this line.

2. At the point corresponding to the number 5, draw a solid dot (or a closed circle). This solid dot indicates that the number 5 is included in the set of numbers that satisfy the inequality (because it's "less than or equal to", not just "less than").

3. Shade or draw an arrow extending to the left of the dot, moving toward the smaller numbers. This shaded region or arrow represents all the numbers that are less than 5, extending indefinitely towards negative infinity.

The resulting visual on a number line will display a solid dot at 5 and a shaded line (or arrow) moving to the left of 5, indicating all values less than or equal to 5 are part of the solution set for the inequality "n ≤ 5."

In a Cartesian coordinate system, an inequality such as "y ≤ x" represents a boundary line (the line y = x) and a region. To graph this inequality:

1. Graph the line y = x. This is a straight line that passes through the origin (0,0) and has a slope of 1 (45 degrees relative to the axes).

2. Because it's a "less than or equal to" inequality, you would draw a solid line for y = x, indicating that points on this line satisfy the inequality.

3. Shade the area below this line (including the line itself), which represents all the points where the y-value is less than or equal to the corresponding x-value.

In both number line and Cartesian graphs, the use of a solid dot or solid line indicates that the value at that point is included in the solution due to the "equal to" part of "less than or equal to."