Question

How do you write in standard form an equation of the line passing through the given point (-3,3) with the given slope 1?

Answer 1

Answer: `x - y + 6 = 0`

Why?

Use the general standard form:
`ax + by + c = 0`

Step1:
in gradient and one point form (also known as point-slope form) you have,
`y - 3 = 1*(x + 3)`

Step2:
arranging this you get,
`x - y + 6 = 0`

Answer 2

`-x+y=0`

Since `y=mx+n` can represent any line, we can use it.

`m` is the slope of our line. The given slope is `1` so `m=1`.

So our formula is formed as `y=1*x+n`

We can now plug the point to this formula to find the value of `n`

`3=1*(-3)+n`
`n=6`

So `y=x+6` represents the line. But we should reform this equality in order to be in the standart form:

`-x+y=6` is the standart form (`ax+by=c`)