Question

What is the equation of a line, in general form, that passes through point (1, -2) and has a slope of 1/3?

Answer 1

`x-3y=7`

Explanation:

The point-slope form for a line passing through `(x,y)=(color(red)a,color(blue)b)` with a slope of `color(green)m` is
`color(white)("XXX")y-color(blue)b=color(green)m(x-color(red)a)` or some modified version of this

Given `(x,y)=(color(red)1,color(blue)(-2))` and a slope of `color(green)(m)` this becomes:
`color(white)("XXX")y-(color(blue)(-2)))=color(green)(1/3)(x-color(red)1)`
or
`color(white)("XXX")y+2=1/3(x-1)`

Typically, you might want to convert this into "standard form": `Ax+By=C` (often with the restrictions `A>=0` and `GCF(A,B,C)=1`).

`y+2=1/3(x-1)`

`color(white)("XXX")rArr 3y+6=x-1`

`color(white)("XXX")rArr 1x-3y=7`