To solve the problem of finding the equation of the line passing through the points [tex]\((-12, -12)\)[/tex] and [tex]\((-12, -4)\)[/tex]:
1. Identify Key Characteristics of the Line:
- The points given are [tex]\((-12, -12)\)[/tex] and [tex]\((-12, -4)\)[/tex].
- Notice that the x-coordinates of both points are the same, specifically [tex]\(x = -12\)[/tex].
2. Nature of the Line:
- Since both points have the same x-coordinate, the line passing through these points does not change its x-value. This means it is a vertical line.
3. Equation of a Vertical Line:
- A vertical line has an equation in the form [tex]\(x = a\)[/tex], where [tex]\(a\)[/tex] is the constant x-coordinate for all points on the line.
- Here, the constant x-coordinate is [tex]\(-12\)[/tex].
4. Write the Equation:
- Therefore, the equation of the line passing through [tex]\((-12, -12)\)[/tex] and [tex]\((-12, -4)\)[/tex] is [tex]\(x = -12\)[/tex].
5. Select the Appropriate Option:
- From the given options:
- a. [tex]\(y = -12\)[/tex]
- b. [tex]\(x = -12\)[/tex]
- c. [tex]\(y = 12\)[/tex]
- d. [tex]\(y = -12x\)[/tex]
- The correct option that matches our equation is:
- b. [tex]\(x = -12\)[/tex]
Thus, the equation of the line passing through the points [tex]\((-12, -12)\)[/tex] and [tex]\((-12, -4)\)[/tex] is [tex]\(x = -12\)[/tex]. The correct choice is option b: [tex]\(x = -12\)[/tex].
