How do you write an equation of the line in standard form with m = 4/3 (-2,-6)?

1 Answer
Oct 28, 2015

First write the equation in slope-point form
then convert to standard form, to get
#color(white)("XXX")4x-3y=10#

Explanation:

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

For the given data this becomes
[1]#color(white)("XXX")y+6 =4/3(x+2)#

Standard form for a linear equation is
#color(white)("XXX")Ax+By=C#
#color(white)("XXXXXXXXX")#for #A,B,C in ZZ# and #A>=0#

Simplifying [1]
[2]#color(white)("XXX")3y+18=4x+8#

Subtracting #(3y+8)# from both sides
[3]#color(white)("XXX")10 = 4x-3y#

Reversing the sides to get standard form:
[4]#color(white)("XXX")4x-3y=10#