How do you write an equation in standard form given a line that passes through (30, –2), (–1, –19)?

1 Answer
Alan P.
May 27, 2015

Given two points the easiest way to write the corresponding linear equation in standard form is to first write it in slope-point form and then re-arrange it to standard form.

Slope-point form
Given the points #(30,-2) and (-1,-19)#
The slope is
#m = (Delta y)/(Delta x) = (-2-(-19))/(30-(-1)) = 17/31#

The slope-point form (using the point #(30,-2)#) is
#(y+2)= (17/31)(x-30)#

Standard form
Standard form of a linear equation is
#Ax+By = C# (usually restricted to #A>=0 and AepsilonZZ#)

#(y+2)= (17/31)(x-30)#

#31y +62 = 17x- 510#

#-17x+31y = -572#

#17x -31y = 572#

standard form

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