Answer :
Graphing the inequality `x ≤ 9` on a number line involves the following steps:
1. Draw a horizontal line to represent the number line.
2. Mark the point corresponding to x=9 on the number line. This can be an arbitrary point, but it should be clearly labeled as '9'.
3. At the point where x=9, draw a solid circle or dot. A solid circle indicates that the value 9 is included in the solution set (since the inequality includes the "less than or equal to" part).
4. Shade or draw a thick line to the left of the point x=9 to indicate that all values less than 9 are also included in the solution.
Here's a textual representation of what the number line would look like:
```plaintext
9
Number Line: ----(===================○------------------------------------>
(included)
```
The area to the left is shaded (here represented by `=`) up to the solid dot, indicating that all values of x that are less than or equal to 9 satisfy the inequality. The solid circle at 9 marks that 9 is also included in the solution set.
If we were to extend this to a two-dimensional graph, we would:
1. Draw two perpendicular lines to represent the x-axis (horizontal) and y-axis (vertical).
2. Mark the point at x=9 on the x-axis.
3. Draw a vertical line at x=9 that spans the graph.
4. Shade the entire area to the left of the line including the line itself. This shading represents all the points (x, y) where the x-coordinate is less than or equal to 9.
Remember that in a two-dimensional plane, the inequality x ≤ 9 means that every point with an x-coordinate of 9 or less is a solution, regardless of its y-coordinate.
1. Draw a horizontal line to represent the number line.
2. Mark the point corresponding to x=9 on the number line. This can be an arbitrary point, but it should be clearly labeled as '9'.
3. At the point where x=9, draw a solid circle or dot. A solid circle indicates that the value 9 is included in the solution set (since the inequality includes the "less than or equal to" part).
4. Shade or draw a thick line to the left of the point x=9 to indicate that all values less than 9 are also included in the solution.
Here's a textual representation of what the number line would look like:
```plaintext
9
Number Line: ----(===================○------------------------------------>
(included)
```
The area to the left is shaded (here represented by `=`) up to the solid dot, indicating that all values of x that are less than or equal to 9 satisfy the inequality. The solid circle at 9 marks that 9 is also included in the solution set.
If we were to extend this to a two-dimensional graph, we would:
1. Draw two perpendicular lines to represent the x-axis (horizontal) and y-axis (vertical).
2. Mark the point at x=9 on the x-axis.
3. Draw a vertical line at x=9 that spans the graph.
4. Shade the entire area to the left of the line including the line itself. This shading represents all the points (x, y) where the x-coordinate is less than or equal to 9.
Remember that in a two-dimensional plane, the inequality x ≤ 9 means that every point with an x-coordinate of 9 or less is a solution, regardless of its y-coordinate.
