What is the equation in point-slope form and slope intercept form for the line given (-6,-4) AND (2,-5)?

1 Answer
Alan P.
Jun 18, 2018

#y+4=(-1/8)(x+6)#

Explanation:

For the given points #(x_1,y_1)=(-6,-4)# and #(x_2,y_2)=(2,-5)#

the slope can be determined as #m=(y_2-y_1)/(x_2-x_1)=(-5-(-4))/(2-(-6))=-1/8#

Using a general variable point #(x,y)# and #(x_1,y_1)# (as above)
we have the slope #m=(y-(-4))/(x-(-6))=(y+4)/(x+6)#

Since the slope is constant for all points on a straight line
#color(white)("XXX")(y+4)/(x+6)=-1/8#

#rArr y+4=(-1/8)(x+6)#

Which is the slope-point form with
#color(white)("XXX")#slope #=(-1/8)#
and
#color(white)("XXX")# the point: #(-6,-4)#

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