To find the equation of the line passing through the points [tex]\((6, 3)\)[/tex] and [tex]\((-4, 3)\)[/tex], let's work through the problem step by step.
1. Identify the coordinates of the points:
- The first point is [tex]\((6, 3)\)[/tex].
- The second point is [tex]\((-4, 3)\)[/tex].
2. Observe the y-coordinates:
- Both points have the same y-coordinate, which is 3.
3. Conclusion about the nature of the line:
- Since the y-coordinates are identical, the line passing through these points is a horizontal line.
4. Equation of a horizontal line:
- For any horizontal line, the y-coordinate is constant for all values of x along the line. This means that regardless of the x-value, the y-value stays the same.
5. Determine the equation:
- Since both points share the y-coordinate 3, the equation of the line is simply [tex]\( y = 3 \)[/tex].
So the equation of the line passing through the points [tex]\((6, 3)\)[/tex] and [tex]\((-4, 3)\)[/tex] is:
[tex]\[ y = 3 \][/tex]
