Question

How do you write an equation in point-slope form for the given (-1, 7), (5, 7)?

Answer 1

Calculate the slope between the two given points and using that slope and either of the points write in point slope form as;
`color(white)("XXXX")` y-7 = 0(x-5)#

Explanation:

Step 1: Determine the slope
Slope of a line between two points `(x_1,y_1)` and `(x_2,y_2)` is
`color(white)("XXXX")` `m = (y_2-y_1)/(x_2-x_1)`

For the given points `(-1,7)` and `(5,7)`, this becomes
`color(white)("XXXX")` `m = (7-7)/(5-(-1)) = 0`

Step 2: Write in slope point form
For a slope of `m` and a point`(hatx,haty)`
the point-slope form is
`color(white)("XXXX")` `y-haty = m(x-hatx)`

If we choose to use `(hatx, haty) = (5, 7)`
and our previously determined value for `m`
this becomes:
`color(white)("XXXX")` `y-7 = 0(x-5)`

Note that this is an unusual form, but it is this the formal "point-slope# version.