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

2 Answers
Alan P.
Mar 24, 2017

#(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)))#

Binayaka C.
Mar 24, 2017

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]

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