What is the equation of the line with slope # m= -7/6 # that passes through # (-7/12,2/3) #?

1 Answer
Apr 12, 2016

#84x+72y=-1#

Explanation:

Using the definition of slope:
#color(white)("XXX")m=(Delta y)/(Delta x)#
and given values:
#color(white)("XXX")#slope: #m=-7/6#,
#color(white)("XXX")#a point: #(-7/12,2/3)#,
and using a variable point #(x,y)# on the required line:

#color(white)("XXX")-7/6=(y-2/3)/(x-(-7/12))#

Multiplying the right side by #12/12# to clear the fractions:
#color(white)("XXX")-7/6 = (12y-8)/(12x+7)#

Then multiply both sides by #6(12x+7)# to clear the denominators
#color(white)("XXX")-7(12x+7)=6(12y-8)#

Simplify
#color(white)("XXX")-84x-49=72y-48#

Add #(84x+48)# to both sides (and flip the sides to write in standard form)
#color(white)("XXX")84x+72y=-1#