How do you write an equation in standard form for the line through (1,3) and (-10,6)?

1 Answer
Alan P.
May 27, 2015

Start by determining the slope of the line through the given points;
then write the equation for the line in point-slope form;
finally convert to standard form.

Slope
The slope of a line is determined by the difference between 2 y-coordinate values divided by the difference between 2 corresponding x-coordinate values.
Given the points #(1,3)# and #(-10,6)#
Slope: #m = (3-6)/(1-(-10)) = - 3/11#

Point-Slope Form
The point-slope form for a line with slope #m# through a point #(y_1,x_1)# is
#(y-y_1) = m(x-x_1)#
For the given values this becomes
#y-3 = (-3/11)(x-1)#

Standard Form for Linear Equation
The standard form for a linear equation is
#Ax+By = C# (usually with the restriction that #A>=0 and Aepsilon ZZ#
#y-3 = (-3/11)(x-1)#

#y = -3/11x +3/11+3#

#3/11x+y = 36/11#

#3x+11y = 36#

(...and our work here is done)

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