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-Point Form of linear equations, the equation of the line passing through $
(4,-2) \text{ and } (6,-3)
$ is
\begin{array}{l}\require{cancel}
y-(-2)=\dfrac{-2-(-3)}{4-6}(x-4)
\\\\
y+2=\dfrac{-2+3}{4-6}(x-4)
\\\\
y+2=\dfrac{1}{-2}(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 form, this is equivalent to $
f(x)=-\dfrac{1}{2}x
$.
