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The points are $\"(-5,$ and $\"(7,$ .

Standard form of line equation using the points $\"(x_{1},$ and $\"(x_{2},$ is $\"(y-y_{1})=\\frac{y_{2}-y_{1}}{x_{2}-x_{1}}(x-x_{1})\"$ .

Substitute $\"(x_{1},$ and $\"(x_{2},$ in the line equation.

$\"(y-10)=\\frac{(-10-10)}{(7-(-5))}(x-(-5))\"$

$\"(y-10)=\\frac{-20}{12}(x+5)\"$

$\"(y-10)=\\frac{-5}{3}(x+5)\"$

$\"y-10=\\frac{-5}{3}x-\\frac{25}{3}\"$

$\"y=\\frac{-5}{3}x-\\frac{25}{3}+10\"$

$\"y=\\frac{-5}{3}x-\\frac{25}{3}+\\frac{30}{3}\"$

$\"y=\\frac{-5}{3}x+\\frac{5}{3}\"$ .

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The function is $\"f(x)=\\frac{-5}{3}x+\\frac{5}{3}\"$ .