Question

Please help me with this question

Answer 1

Parallel line:
`y=4x+33`

Perpendicular line: y =
`(-1)/(4)x-1`

Explanation:

From the given equation
`y=4x-2`, the number multiplied by
`x` is the slope of that equation, so the slope is 4 in this case.

Let's use the point slope form in this question:

`{y-y__1}=m({x-x__1})`

where
`{x__1}` and
`y__1` are the given points in your question:

`{x__1}=-8`

`{y__1} = 1`

and m is the slope.

Parallel line:

Since parallel means the same slope as the given equation, we put
`m = 4` first.

`{y-1}=4({x-(-8)})`

`y=4x+33`

This is the equation that is parallel to
`y=4x-2` and also passes through
`(-8,1)`.

Perpendicular line:

Since perpendicular means exactly 90° with the given equation, multiplying their slopes and the product will always be
`-1`.

Let's find m first,

`4* m = -1`

`m = (-1)/(4)`

Now using the same point slope form with the same
`x__1` and
`y__1`:

`{y-y__1}=m({x-x__1})`

`{y-1}=(-1)/(4) ({x-(-8)})`

`y=(-1)/(4)x-1`

This is the equation that is perpendicular to
`y=4x-2` and also passes through
`(-8,1)`.