How do you find the equation of the line that goes through (-3, 1) and (1, -3)?

1 Answer
Jacq
Oct 4, 2017

Equation: # x+y+2=0#

Explanation:

The two point are #(-3, 1)# and #(1, -3)#.

You can find the equation by using the point-gradient formula, #y-y_1=m(x-x_1)#.

To do this, we first need to find the gradient of the line. This can be done using the gradient formula:

#(y_1-y_2)/(x_1-x_2)#
#= (1-(-3))/(-3-1)#
#=4/-4#
#=-1#

We now have the gradient, represented by #m# in the point-gradient formula, and can choose any one of the two coordinates given by the question to sub into this formula. Let's go with #(-3, 1)#.

#y-y_1=m(x-x_1)#
#y-1=-1(x-(-3))#
#y-1=-1(x+3))#
#y-1=-x-3#
#therefore y=-x-2#

Or, if the question asks for the equation in general form, move all the values to one side so that the coefficient of #x# is positive and the equation equals to #0#:
#y=-x-2#
#therefore x+y+2=0#

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