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

Mar 16, 2018

$x + y = 0$

#### Explanation:

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

As $f \left(- 1\right) = 1$, the line passes through $\left(- 1 , 1\right)$

and as $f \left(1\right) = - 1$, the line passes through $\left(1 , - 1\right)$

As equation of line passing through $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ is

$\frac{y - {y}_{1}}{{y}_{2} - {y}_{1}} = \frac{x - {x}_{1}}{{x}_{2} - {x}_{1}}$

Hence, equation of line passing through $\left(- 1 , 1\right)$ and $\left(1 , - 1\right)$ is

$\frac{y - 1}{- 1 - 1} = \frac{x - \left(- 1\right)}{1 - \left(- 1\right)}$

or $\frac{y - 1}{- 2} = \frac{x + 1}{2}$

or $y - 1 = - x - 1$

or $x + y = 0$