Answer:
The equation of the line is [tex]y=-4x-9.[/tex]
Step-by-step explanation:
If we want our line to be parallel to [tex]y=-4x+2[/tex], then it must have the same slope.
The slope of [tex]y=-4x+2[/tex] is -4, thus the equation of our parallel line is of the form:
[tex]y=-4x+b[/tex]
Where [tex]b[/tex] is the y-intercept of the line.
Now we know that the point [tex](-2,-1)[/tex] lies on the parallel line thus it must be true that:
[tex]-1=-4(-2)+b[/tex]
From this equation we get the value of [tex]b:[/tex]
[tex]b=-1+4(-2)=-9[/tex]
Thus the equation of our parallel line becomes:
[tex]\boxed{y=-4x-9.}[/tex]
