Question

How do you write an equation of a line through (6, 2); parallel to `4x-y=3`?

Answer 1

I got: `4x-y=22`

Explanation:

We can use the general expression for a line through a point of coordinates `(x_0,y_0)` and slope `m` as:

`y-y_0=m(x-x_0)`

The slope must be the same of the slope of the original line in order to be parallel.

The original line can be written (collecting `y`) as:
`y=4x-3`
where the slope will be: `m=4` (the coefficient of `x`):
so we have:
`y-2=4(x-6)`
`y=4x-24+2`
`y=4x-22`
or
`4x-y=22`