Answer
$\text{a) }
f(x)=\dfrac{2}{5}x+\dfrac{9}{5}
\\\\\text{b) }
f(3)=3$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of equality to isolate $y$ in the given equation, $
-2x+5y=9
,$ 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}
-2x+5y=9
\\\\
5y=2x+9
\\\\
\dfrac{5y}{5}=\dfrac{2x}{5}+\dfrac{9}{5}
\\\\
y=\dfrac{2}{5}x+\dfrac{9}{5}
.\end{array}
Using $y=f(x),$ the function notation of the equation above is $
f(x)=\dfrac{2}{5}x+\dfrac{9}{5}
.$
Substituting $x$ with $
3
,$ then
\begin{array}{l}\require{cancel}
f(x)=\dfrac{2}{5}x+\dfrac{9}{5}
\\\\
f(3)=\dfrac{2}{5}(3)+\dfrac{9}{5}
\\\\
f(3)=\dfrac{6}{5}+\dfrac{9}{5}
\\\\
f(3)=\dfrac{15}{5}
\\\\
f(3)=3
.\end{array}
Hence,
\begin{array}{l}\require{cancel}
\text{a) }
f(x)=\dfrac{2}{5}x+\dfrac{9}{5}
\\\\\text{b) }
f(3)=3
.\end{array}
