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

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Answer 1 · 2018-03-16T05:42:52

$x + y = 0$ $x+y=0$

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

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

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

As equation of line passing through $(x_{1}, y_{1})$ $(x_1,y_1)$ and $(x_{2}, y_{2})$ $(x_2,y_2)$ is

$\frac{y - y_{1}}{y_{2} - y_{1}} = \frac{x - x_{1}}{x_{2} - x_{1}}$ $(y-y_1)/(y_2-y_1)=(x-x_1)/(x_2-x_1)$

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

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

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

or $y - 1 = - x - 1$ $y-1=-x-1$

or $x + y = 0$ $x+y=0$

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