The points are $\"(1,$ and $\"(5,$ .

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.

$\"(y-(-3))=\\frac{7-(-3)}{5-1}(x-1)\"$

$\"(y+3)=\\frac{7+3}{4}(x-1)\"$

$\"(y+3)=\\frac{10}{4}(x-1)\"$

$\"(y+3)=\\frac{10}{4}x-\\frac{10}{4}\"$

$\"y=\\frac{5}{2}x-\\frac{5}{2}-3\"$

$\"y=\\frac{5}{2}x-(\\frac{5}{2}+3)\"$

$\"y=\\frac{5}{2}x-(\\frac{5+6}{2})\"$

$\"y=\\frac{5}{2}x-(\\frac{11}{2})\"$ .

The function is $\"f(x)=\\frac{5}{2}x-(\\frac{11}{2})\"$ .