Answer
$f(x)=-2x+10$
Work Step by Step
We are given the points $(7,-4)$ and $(2,6)$. We can use the slope formula to find the slope of a line going through these points.
$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{6-(-4)}{2-7}=\frac{10}{-5}=-2$
Next, we can use this slope and one of the given points to write the line in the point slope form $y-y_{1}=m(x-x_{1})$.
$f(x)=y+4=-2(x-7)=-2x+14$
Subtract 4 from both sides.
$f(x)=-2x+10$
