Sure, let's graph the line [tex]\( x = -5 \)[/tex].
Here's a detailed step-by-step solution:
1. Understanding the Equation:
- The equation [tex]\( x = -5 \)[/tex] represents a vertical line.
- No matter what value [tex]\( y \)[/tex] takes, the value of [tex]\( x \)[/tex] will always be [tex]\(-5\)[/tex].
2. Choosing a Range for [tex]\( y \)[/tex]:
- For practical purposes, let's consider a limited range for [tex]\( y \)[/tex].
- We can choose integer values for [tex]\( y \)[/tex] from [tex]\(-10\)[/tex] to [tex]\(10\)[/tex].
3. Generating Points:
- Since [tex]\( x \)[/tex] is always [tex]\(-5\)[/tex], let's create points by varying [tex]\( y \)[/tex] within the chosen range.
- The pairs [tex]\((x, y)\)[/tex] where [tex]\( x = -5 \)[/tex] and [tex]\( y \)[/tex] ranges from [tex]\(-10\)[/tex] to [tex]\(10\)[/tex] are:
1. [tex]\( (-5, -10) \)[/tex]
2. [tex]\( (-5, -9) \)[/tex]
3. [tex]\( (-5, -8) \)[/tex]
4. [tex]\( (-5, -7) \)[/tex]
5. [tex]\( (-5, -6) \)[/tex]
6. [tex]\( (-5, -5) \)[/tex]
7. [tex]\( (-5, -4) \)[/tex]
8. [tex]\( (-5, -3) \)[/tex]
9. [tex]\( (-5, -2) \)[/tex]
10. [tex]\( (-5, -1) \)[/tex]
11. [tex]\( (-5, 0) \)[/tex]
12. [tex]\( (-5, 1) \)[/tex]
13. [tex]\( (-5, 2) \)[/tex]
14. [tex]\( (-5, 3) \)[/tex]
15. [tex]\( (-5, 4) \)[/tex]
16. [tex]\( (-5, 5) \)[/tex]
17. [tex]\( (-5, 6) \)[/tex]
18. [tex]\( (-5, 7) \)[/tex]
19. [tex]\( (-5, 8) \)[/tex]
20. [tex]\( (-5, 9) \)[/tex]
21. [tex]\( (-5, 10) \)[/tex]
4. Graphing the Line:
- On a two-dimensional coordinate plane:
- Plot each point from the above list.
- All these points will align vertically.
- Draw a straight vertical line through these points.
The resulting graph should be a straight vertical line intersecting the x-axis at [tex]\( x = -5 \)[/tex], extending infinitely in both the upward and downward directions through the plotted points.
