# Find the linear function with the following properties. f(4)=9 f(-8)=11

Find the linear function with the following properties.
$f\left(4\right)=9\phantom{\rule{0ex}{0ex}}f\left(-8\right)=11$
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Solution:
$f\left(4\right)=9\phantom{\rule{0ex}{0ex}}f\left(-8\right)=11\phantom{\rule{0ex}{0ex}}\left({x}_{1},{y}_{1}\right)=\left(4,9\right)\phantom{\rule{0ex}{0ex}}\left({x}_{2},{y}_{2}\right)=\left(-8,11\right)\phantom{\rule{0ex}{0ex}}y-9=\left(\frac{11-9}{-8-4}\right)\left(x-4\right)\phantom{\rule{0ex}{0ex}}y-9=\frac{-1}{6}\left(x-4\right)\phantom{\rule{0ex}{0ex}}y=\frac{-1}{6}x+\frac{4}{6}+9\phantom{\rule{0ex}{0ex}}y=\frac{-1}{6}x+\frac{29}{3}$