To determine the equations of the lines that are parallel to the given line [tex]\( y = -2 \)[/tex] and pass through the given points, follow these steps:
1. Understand the given line equation:
The equation [tex]\( y = -2 \)[/tex] represents a horizontal line where the y-coordinate is always -2, irrespective of the x-coordinate.
2. Identify lines parallel to the given line:
Lines that are parallel to [tex]\( y = -2 \)[/tex] must also be horizontal. A horizontal line's equation is generally in the form [tex]\( y = c \)[/tex], where [tex]\( c \)[/tex] is a constant.
3. Find the equations of the lines that pass through the given points:
- Point (-2, -4):
- Since the line must be parallel to [tex]\( y = -2 \)[/tex], it must also be horizontal.
- It needs to pass through the point (-2, -4), where [tex]\( y = -4 \)[/tex].
- Therefore, the equation of this line is [tex]\( y = -4 \)[/tex].
- Point (-4, -4):
- Similarly, this line must also be horizontal and pass through the point (-4, -4).
- Since the y-coordinate of this point is -4, the equation of the line will also be [tex]\( y = -4 \)[/tex].
4. Conclusion:
The equations of the lines that are parallel to [tex]\( y = -2 \)[/tex] and pass through the points (-2, -4) and (-4, -4) are both [tex]\( y = -4 \)[/tex].
Therefore, the equations of the parallel lines through the given points are:
[tex]\[ y = -4 \text{ and } y = -4 \][/tex]
