Question

How do you write the equation of the line in the form AX+BY=C if (2,5) ; m=3/1?

Answer 1

#3x-1y=1

Explanation:

Given the point `(2,5)` and the slope `m=3/1`
we can start with the slope-point form for the line:
`color(white)("XXX")(y-haty) = m(x-hatx)`
or, for the given values:
`color(white)("XXX")(y-5) = 3(x-2)`

Simplifying
`color(white)("XXX")y-5 = 3x-6`

Rearranging so variables are on the left and constant is on the right:
`color(white)("XXX")-3x + y = -1`

There is normally a requirement that `A` of `Ax+By=C` be `>=0`
In this case:
`color(white)("XXX")3x-1y=1`