Question

How do you write an equation in point-slope form for the given (6, 1), (-4. 1)?

Answer 1

`y-1 = 0*(x-6)color(white)("XXXX")`in explicit point slope form
or`color(white)("XXXXX")y=1` in more common form.

Explanation:

Given `(6,1)` and `(-4,1)`
the change in `y` is zero
and
since the slope is defined as
`color(white)("XXX")m = ("change in y")/("change in x")`
The slope is
`color(white)("XXX")m = 0`

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

We have a slope of `m=0` and can use `(hatx,haty) = (6,1)`
to obtain the explicit slope-point form shown in the answer.