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

Question

4243 views around the world

You can reuse this answer
Creative Commons License

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 $x+y=0$

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