Answer
$f(x)=-\dfrac{1}{2}x$
Work Step by Step
Using $y-y_1=\dfrac{y_1-y_2}{x_1-x_2}(x-x_1)$ or the Two-PointForm, the equation of the line passing through $( 4,-2 )$ and $( 6,-3 )$ is \begin{array}{l} y-(-2)=\dfrac{-2-(-3)}{4-6}(x-4)
\\\\
y+2=\dfrac{1}{-2}(x-4)
\\\\
y+2=-\dfrac{1}{2}x+2
\\\\
y=-\dfrac{1}{2}x+2-2
\\\\
y=-\dfrac{1}{2}x
.\end{array}
In function notation, this is equivalent to $
f(x)=-\dfrac{1}{2}x
.$
