Question

What is the equation of the line with slope `m= -5/6` that passes through `(-5/12,4/3)`?

Answer 1

`60x+72y=71`

Explanation:

Starting with the general "slope-point" form:
`color(white)("XXX")(y-haty)=m(x-hatx)`
for a line with slope `m` through the point `(hatx,haty)`

we can insert the given values `m=(-5/6)` and `(hatx,haty)=(-5/12,4/3)`
to get
`color(white)("XXX")(y-4/3)=(-5/6)(x+5/12)`

Theoretically we could claim that this is the answer but it's ugly, so let's convert it into "standard form" (`Ax+By=C`)

We can see by looking at the right side that to clear the denominators we will need to multiply both sides by `72` (i.e. `6xx12`)
`color(white)("XXX")72y-96 = -60x-25`

Adding `60x+96` to both sides to shift the `x` term to the left side and the constant to the right:
`color(white)("XXX")60x+72y = 71`