Answer
$\text{a) }
f(x)=\dfrac{1}{4}x-2
\\\\\text{b) }
f(3)=-\dfrac{5}{4}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of equality to isolate $y$ in the given equation, $
x-4y=8
,$ and then express in function notation. Then find $f(3)$ by substituting $x$ with $3.$
$\bf{\text{Solution Details:}}$
Using the properties of equality, the given equation is equivalent to
\begin{array}{l}\require{cancel}
x-4y=8
\\\\
-4y=-x+8
\\\\
\dfrac{-4y}{-4}=\dfrac{-x}{{-4}}+\dfrac{8}{-4}
\\\\
y=\dfrac{1}{4}x-2
.\end{array}
Using $y=f(x),$ the function notation of the equation above is $
f(x)=\dfrac{1}{4}x-2
.$
Substituting $x$ with $
3
,$ then
\begin{array}{l}\require{cancel}
f(x)=\dfrac{1}{4}x-2
\\\\
f(3)=\dfrac{1}{4}(3)-2
\\\\
f(3)=\dfrac{3}{4}-2
\\\\
f(3)=\dfrac{3}{4}-\dfrac{8}{4}
\\\\
f(3)=-\dfrac{5}{4}
.\end{array}
Hence,
\begin{array}{l}\require{cancel}
\text{a) }
f(x)=\dfrac{1}{4}x-2
\\\\\text{b) }
f(3)=-\dfrac{5}{4}
.\end{array}