How do you write an equation in standard form given a line that passes through (-9,-2) and (7,9)?

1 Answer
Alan P.
May 30, 2015

The easiest way to solve this requirement is to:

  • Step 1: write the equation in point-slope form
  • Step 2: convert the point-slope form into standard form

Step1: point-slope form
Given the two points #(-9,-2)# and #(7,9)#
the slope is given as
#color(white)("XXXXX")##m=(Delta y)/(Delta x) = (9-(-2))/(7-(-9)) = 11/16#
Using this slope and the point #(7,9)# (we could use either given point)
the point-slope form is
#color(white)("XXXXX")##(y-9) = 11/16(x-7)#

Step 2: Convert to standard form
Standard form is (normally) expressed as
#color(white)("XXXXX")##Ax+By=C# with #A>=0 and AepsilonZZ#
Starting with
#color(white)("XXXXX")##(y-9) = 11/16(x-7)#
we can write
#color(white)("XXXXX")##16(y-9) = 11(x-7)#

#color(white)("XXXXX")##16y - 144 = 11x -77#

#11x -16y = -67##color(white)("XXXXX")#(standard form)

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