How do you write an equation for a line given #f(-1)=1# and #f(1)=-1#?

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Answer 1 · 2018-03-16T05:42:52

#x+y=0#

It os apparent that the line is #y=-x# or #x+y=0#. The more formal proof is as follows:

As #f(-1)=1#, the line passes through #(-1,1)#

and as #f(1)=-1#, the line passes through #(1,-1)#

As equation of line passing through #(x_1,y_1)# and #(x_2,y_2)# is

#(y-y_1)/(y_2-y_1)=(x-x_1)/(x_2-x_1)#

Hence, equation of line passing through #(-1,1)# and #(1,-1)# is

#(y-1)/(-1-1)=(x-(-1))/(1-(-1))#

or #(y-1)/(-2)=(x+1)/2#

or #y-1=-x-1#

or #x+y=0#