Question

How do you write an equation of the line with (4,2);m = -5/3?

Answer 1

`y = (-5/3)(x-4)+2`
or
`3y = 26-5x`
etc.

Explanation:

Slope of a straight line is `m= (y-haty)/(x-hatx)` (by definition)

With `(hatx,haty) = (4,2)` and `m=(-5/3)`
this becomes
`color(white)("XXXX")` `-5/3 = (y-2)/(x-4)`
which can be rewritten in numerous forms:
`color(white)("XXXX")` `(y-2) = (-5/3)(x-4)`

`color(white)("XXXX")` `y = (-5/3)(x-4)+2`

`color(white)("XXXX")` `3y = -5x+26`