Question

What is the equation of the line between `(-1,14)` and `(14,4)`?

Answer 1

`2x+3y=40`

Explanation:

Given the points `(-1,14)` and `(14,4)`
the slope is
`color(white)("XXX")m=(Delta y)/(Delta x) = (14-4)/(-1-14) = 10/(-15) = -2/3`

The slope-point form of the equation for a line with slope `m` through a point `(hatx,haty)` is
`color(white)("XXX")(y-haty)=m(x-hatx)`

Arbitrarily choosing `(hatx,haty)= (14,4)` [note that either point would work]:
`color(white)("XXX")(y-4)=-2/3(x-14)`
and this is one possible solution to the question asked.

However let's put it into standard form (`Ax+By=C`)

`color(white)("XXX")3(y-4)=-2(x-14)`

`color(white)("XXX")3y-12=-2x+28`

`color(white)("XXX")2x+3y=40`