To determine the equation of the line that passes through the points [tex]\((3, 3)\)[/tex] and [tex]\((3, -3)\)[/tex], let's analyze the given points step-by-step:
1. Identify the coordinates of the points:
- Point 1: [tex]\((3, 3)\)[/tex]
- Point 2: [tex]\((3, -3)\)[/tex]
2. Determine the type of line:
- Notice that both points have the same x-coordinate (3). This means that the line passing through these points is a vertical line.
3. Characteristics of vertical lines:
- Vertical lines have an undefined slope because the difference in x-coordinates (denominator in the slope formula) is zero, which results in division by zero.
- The equation of a vertical line can be written in the form [tex]\(x = a\)[/tex], where [tex]\(a\)[/tex] is the constant x-coordinate for all points on the line.
4. Formulate the equation:
- Since both points through which the line passes have an x-coordinate of 3, the equation of the line is [tex]\(x = 3\)[/tex].
Therefore, the equation of the line that passes through the points [tex]\((3, 3)\)[/tex] and [tex]\((3, -3)\)[/tex] is:
[tex]$x = 3.$[/tex]
