Answer:
y = - 4x - 2 is the required equation of the line.
Step-by-step explanation:
Equation of two parallel lines differ only by a constant.
If the equation of a line is [tex]$ ax + by + l = 0 $[/tex] then the equation of the line parallel to it is given by [tex]$ ax + by + k = 0 $[/tex].
Note that only the constants differ in both the equations.
The given equation is: y = - 4x - 2
This is equivalent to 4x + y + 2 = 0.
Therefore, the equation of the line parallel to the given line will be:
4x + y + k = 0.
We are also given the point which passes through the line. We can substitute it to determine the value of 'k'.
Substituting (- 2, 6), we get:
4(-2) + 6 + k = 0
⇒ - 8 + 6 + k = 0
⇒ k = 2
Hence, the equation of the required line is: y = - 4x - 2
