# What is the equation written in point slope form if f(6)=0 and f(0)=6?

Oct 29, 2014

Since

$\left\{\begin{matrix}f \left(6\right) = 0 R i g h t a r r o w \left({x}_{1} {y}_{1}\right) = \left(6 0\right) \\ f \left(0\right) = 6 R i g h t a r r o w \left({x}_{2} {y}_{2}\right) = \left(0 6\right)\end{matrix}\right.$,

the slope $m$ can be found by the slope formula

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{6 - 0}{0 - 6} = - 1$.

By Point-Slope Form $y - {y}_{1} = m \left(x - {x}_{1}\right)$, we have

$y - 0 = - 1 \left(x - 6\right)$.

I hope that this was helpful.