Question

How do you write `y-1/4 = -3( x + 1/4 )` in standard form?

Answer 1

`12x+4y = -2`
Note: I'm assuming that by "standard form", you mean `Ax+By = C`.

Explanation:

First we begin by distributing the -3 on the right side of the equation:
`y-1/4 = -3x-3/4`
From here, there are a few ways you can proceed. You can work with the fractions, but I prefer to get rid of them, in this case by multiplying by `4`:
`4y-1 = -12x-3`
Now it's just a little algebra:
`4y = -12x-2` (adding `1` to both sides)
`12x+4y = -2` (adding `12x` to both sides)

This is the official standard form of a linear equation, but most of the time you see them in slope-intercept form, `y = mx+b`. If this is what you meant by "standard form", or if you just want to know just in case, with a little work you can get there:
`12x+4y = -2`
`4y = -2-12x` (subtracting `12x` from both sides)
`y = -3x-1/2` (dividing by `4`)
And there you go.