To find the equation of a line that is parallel to [tex]\( y = -2 \)[/tex] and passes through the point [tex]\( (-4, -4) \)[/tex], follow these steps:
1. Understand the given line: The line [tex]\( y = -2 \)[/tex] is a horizontal line. Horizontal lines have the same [tex]\( y \)[/tex]-coordinate for all [tex]\( x \)[/tex]-values. Therefore, any line parallel to [tex]\( y = -2 \)[/tex] must also be a horizontal line.
2. Characteristic of parallel lines: Since horizontal lines are parallel if they have the same slope (which is zero for a horizontal line), the equation of any line parallel to [tex]\( y = -2 \)[/tex] will be in the form of [tex]\( y = c \)[/tex], where [tex]\( c \)[/tex] is a constant.
3. Determine the parallel line's constant [tex]\( c \)[/tex]: The parallel line must pass through the given point [tex]\( (-4, -4) \)[/tex]. For the line to pass through this point, the [tex]\( y \)[/tex]-coordinate of the line must equal [tex]\(-4\)[/tex].
Therefore, the equation of a horizontal line that passes through the point [tex]\( (-4, -4) \)[/tex] is:
[tex]\[ y = -4 \][/tex]
This means the equation of the line parallel to [tex]\( y = -2 \)[/tex] and passing through [tex]\( (-4, -4) \)[/tex] is:
[tex]\[ y = -4 \][/tex]
