Question

How do you write an equation in standard form for a line passing through (–2, 8) with a slope of 2?

Answer 1

Standard form for a line is `ax+by=c`

Start in point slope form: `y-y_1 = m(x-x_1)` where `(x_1, y_1)` is a point on the line and `m` is the slope.

`y-8=2(x-(-2))`

Now simplify and remove the parentheses (by distributing the `2`):

`y-8=2(x +2)`

`y-8=2x +4`

To get slope-intercept form, we would get the `y` alone by adding `8`.

But we've been asked for standard from, so we need to get the `x` and `y` together and everything else on the other side:

Subtract `2x` (or add `-2x` -- it's the same) and add `8` to get:

`y-2x=4+8=10`

We need the `x` term first, (remember the `-2` is stuck to the `x`) so:

`-2x+y=12`

If you don't like the `-` sign in front of the `x`, you can multiply both sides by `-1` (although this will put a `-` sign in front of the `12`)

`-1(-2x+y) = (-1)(12)`

`2x-y=-12`

Answer 2

The most commonly accepted version of "standard form" for a linear equation in two unknowns is:
`Ax+By=C` for some constants `A, B, C`

The equation of a line through `(-2,8)` with a slope of `2` is
`(y-8)/(x-(-2)) = 2`

`y-8 = 2x+4`

`-2x+y = 12`