Answer: The correct option is (C) [tex]y=-6.[/tex]
Step-by-step explanation: We are given to find the equation of the line that is parallel to the given line in the graph and passes through the point (−4,−6 ).
We can see from the graph that
the line passes through the points (-8, 4) and (8, 4). So, the slope of the graphed line is
[tex]m=\dfrac{4-4}{8-(-8)}\\\\\\\Rightarrow m=\dfrac{0}{16}\\\\\Rightarrow m=0.[/tex]
The line parallel to the graphed line will also have slope m = 0 because parallel lines have same slopes.
Since the new line passes through the point (-4, -6), so its equation will be
[tex]y-(-6)=m(x-(-4))\\\\\Rightarrow y+6=0(x+4)\\\\\Rightarrow y+6=0\\\\\Rightarrow y=-6.[/tex]
Thus, the required equation of the line is [tex]y=-6.[/tex]
Option (C) is CORRECT.
