Question

How do you write an equation in standard form given point (0,0) and slope 1/3?

Answer 1

`1x-3y=0`

Explanation:

For a line with slope `color(green)(1/3)` through the point `(x,y)=(color(red)0,color(blue)0)`
the slope-point form is
`color(white)("XXX")y-color(blue)0=color(green)(1/3)(x-color(red)0)`
which simplifies as
`color(white)("XXX")3y=1x`

Standard form for a linear equation is
`color(white)("XXX")Ax+By=C` with `A,B,C in ZZ` and `A>=0`

To convert `3y=1x` into standard form
subtract `3y` from both sides:
`color(white)("XXX")0=1x-3y`
then reverse the left and right hand sides
`color(white)("XXX")1x-3y=0`