Answer
A function
$f(x)=\dfrac{4x}{5}-3$
Domain: $(-\infty,\infty)$
Range: $(-\infty,\infty)$
Graph of $4x-5y=15$
Work Step by Step
The given equation, $
4x-5y=15
$, is a line. To graph this equation, use substitution to find two points that are on the line defined by the equation.
Using substitution,
\begin{array}{l|r}
\text{If }x=0: & \text{If }x=5:
\\\\
4(0)-5y=15 & 4(5)-5y=15
\\
0-5y=15 & 20-5y=15
\\
-5y=15 & -5y=15-20
\\\\
y=\dfrac{15}{-5} & -5y=-5
\\\\
y=-3 & y=\dfrac{-5}{-5}
\\\\
& y=1
.\end{array}
Therefore, the points $(0,-3)$ and $(5,1)$ are on the line defined by the given equation. Plotting these points and connecting these give the graph of $4x-5y=15$ (see graph above).
Based on the graph above, the equation is a function since it will pass the Vertical Line Test. That is, a vertical line drawn anywhere will intersect the graph above in at most $1$ point.
Hence, the function notation of the given equation is $
f(x)=\dfrac{4x}{5}-3
$.
Using the graph, the domain (values of $x$ used in the graph) is the set of all real numbers. The range (values of $y$ used in the graph) is the set of all real numbers.
