Question

What is the equation of the line that passes through (8,4) and parallel to `4x - y = 8`?

Answer 1

4x-y=28

Explanation:

to be parallel with `y=4x-8`, it is `y=4x+a`.
(8,4)=>`32+a=4`,`a=-28` so `y=4x-28,4x-y=28`

Answer 2

`y=4x-28`

Explanation:

`4x-y=8` is the same as: `y=4x-8`

So the slope is `4` and the y-intercept is `-8`

The equation of the line we are trying to find is parallel to this line, and parallel lines have equivalent slopes.

So we need a line with the equation:

`y=4x+b` where `b` is the y-intercept of this parallel line.

Since the line goes through `(8,4)` we can plug in those values for x and y:

`(4)=4(8)+b`

`4=32+b`
`-28=b`

So equation is: `y=4x-28`