Question

What is the equation of the line passing through `(5,8)` and `(12,3)`?

Answer 1

`5x+7y=81`

Explanation:

The slope between `(5,8)` and `(12,3)` is
`color(white)("XXX")m=(3-8)/(12-5)= -5/7`

Using this slope and one of the points (I picked `(5,8)` but either would work)
we can apply the slope-point form: `(y-bary)=m(x-barx)` to get
`color(white)("XXX")y-8 = (-5/7)(x-5)`
which is a perfectly valid answer to the given question.

However, let's continue and convert it into standard form: `ax+by=c`

`color(white)("XXX")7(y-8)=-5(x-5)`

`color(white)("XXX")7y-56=-5x+25`

`color(white)("XXX")5x+7y=81`