How do you find a standard form equation for the line with P= (-5,-5) and Q= (-3,-2)?

1 Answer
Alan P.
Feb 5, 2017

#3x-2y=-5#
(see below for method)

Explanation:

Step 1: Develop a slope-point form for the line
The slope of a line between two points is defined as:
#color(white)("XX")#The difference between the #y# coordinate values
#color(white)("XX")#divided by the corresponding difference between the #x# coordinates.
#color(white)("XXXXX")m=(Deltay)/(Deltax)= (-2-(-5))/(-3-(-5))=3/2#

This relationship must hold for any arbitrary point #(x,y)# on the line;
so
#color(white)("XXXXX")m=(y-(-5))/(x-(-5))=(y+5)/(x+5)#

Therefore
#color(white)("XXXXX")(y+5)/(x+5)=3/2#
or
#color(white)("XXXXX")y+5 =3/2(x+5)#

Step 2: Convert the slope-point form into standard form
Note that the standard form for a linear equation is
#color(white)("XX")Ax+By=C# with constants #A, B, C# and #A>=0#

If
#color(white)("XXXXX")y+5=3/2(x+5)#
then
#color(white)("XXXXX")2(y+5)=3(x+5)#
#rArr#
#color(white)("XXXXX")2y+10=3x+15#
#rArr#
#color(white)("XXXXX")-5=3x-2y#
or
#color(white)("XXXXX")3x-2y=-5#

Here is the graph for verification purposes:
enter image source here

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