Question

How do you write the equation in point slope form given (-2,-8) and slope 5/6?

Answer 1

`(y+8)/(x+2)=5/6`

Explanation:

Given a point `(color(red)a,color(blue)b)` and a slope of `color(green)m`
the slope-point form may be written as:
`color(white)("XXX")(y-color(blue)b)/(x-color(red)a) = color(green)m`
or (equivalently)
`color(white)("XXX")y-color(blue)b=color(green)m(x-color(red)a)`

Substituting `(color(red)(-2),color(blue)(-8))` for `(color(red)a,color(blue)b)` and `color(green)(5/6)` for `color(green)m`
we get
`color(white)("XXX")(ycolor(blue)(+8))/(xcolor(red)(+2))=color(green)(5/6)`
or
`color(white)("XXX")ycolor(blue)(+8)=color(green)(5/6)(xcolor(red)(+2))`

Warning: Check with your instructor; he/she may want the factors left in explicit point form, namely: `(y-color(blue)(""(-8)))` and `(x-color(red)(""(-2)))`

Answer 2

The equation of the line is `y = 5/6x -6 1/3`

Explanation:

Let the equation of the line be `y=mx+c ; m= 5/6 :. y=5/6x+c`.

The point `(-2,-8)` will satisfy the equation. `:. -8 = 5/6*(-2) +c :. c = 10/6-8 = -38/6 = -19/3 = -6 1/3 :. y = 5/6x -6 1/3`

The equation of the line is `y = 5/6x -6 1/3` [Ans]