Answer:
Parallel line: [tex]y=4x+33[/tex]
Perpendicular line: y = [tex]\frac{-1}{4}x-1[/tex]
Step-by-step explanation:
From the given equation [tex]y=4x-2[/tex], the number multiplied by [tex]x[/tex] is the slope of that equation, so the slope is 4 in this case.
Let's use the point slope form in this question:
[tex]{y-y__1}=m({x-x__1})[/tex]
where [tex]{x__1}[/tex] and [tex]y__1[/tex] are the given points in your question:
[tex]{x__1}=-8[/tex]
[tex]{y__1} = 1[/tex]
and m is the slope.
Parallel line:
Since parallel means the same slope as the given equation, we put [tex]m = 4[/tex] first.
[tex]{y-1}=4({x-(-8)})[/tex]
[tex]y=4x+33[/tex]
This is the equation that is parallel to [tex]y=4x-2[/tex] and also passes through [tex](-8,1)[/tex].
Perpendicular line:
Since perpendicular means exactly 90° with the given equation, multiplying their slopes and the product will always be [tex]-1[/tex].
Let's find m first,
[tex]4* m = -1[/tex]
[tex]m = \frac{-1}{4}[/tex]
Now using the same point slope form with the same [tex]x__1[/tex] and [tex]y__1[/tex]:
[tex]{y-y__1}=m({x-x__1})[/tex]
[tex]{y-1}=\frac{-1}{4} ({x-(-8)})[/tex]
[tex]y=\frac{-1}{4}x-1[/tex]
This is the equation that is perpendicular to [tex]y=4x-2[/tex] and also passes through [tex](-8,1)[/tex].
