Parallel lines have the same a slope.
The slope-intercept form:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
We have y = -2x - 6 → the slope m = -2. Therefore we have the equation of a line:
[tex]y = -2x + b[/tex]
Put the coordinates of the point (-4, 1) to the equation:
[tex]1=-2(-4)+b[/tex]
[tex]1=8+b[/tex] subtract 8 from both sides
[tex]-7=b\to b=-7[/tex]
Answer: y = -2x - 7
