What is the equation of the line with slope # m= -5/6 # that passes through # (-5/12,4/3) #?

1 Answer
Alan P.
Dec 1, 2015

#60x+72y=71#

Explanation:

Starting with the general "slope-point" form:
#color(white)("XXX")(y-haty)=m(x-hatx)#
for a line with slope #m# through the point #(hatx,haty)#

we can insert the given values #m=(-5/6)# and #(hatx,haty)=(-5/12,4/3)#
to get
#color(white)("XXX")(y-4/3)=(-5/6)(x+5/12)#

Theoretically we could claim that this is the answer but it's ugly, so let's convert it into "standard form" (#Ax+By=C#)

We can see by looking at the right side that to clear the denominators we will need to multiply both sides by #72# (i.e. #6xx12#)
#color(white)("XXX")72y-96 = -60x-25#

Adding #60x+96# to both sides to shift the #x# term to the left side and the constant to the right:
#color(white)("XXX")60x+72y = 71#

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