Answer
see graph
Work Step by Step
Changing the given inequality, $
5x-3y\lt10
,$ to equality and then isolating $y$ result to
\begin{array}{l}\require{cancel}
5x-3y=10
\\\\
-3y=-5x+10
\\\\
y=\dfrac{-5}{-3}x+\dfrac{10}{-3}
\\\\
y=\dfrac{5}{3}x-\dfrac{10}{3}
.\end{array}
Use the table of values below to graph this line.
Since the inequality used is "$
\lt
$", use a broken line.
Using the testpoint $(
0,0
)$, then
\begin{array}{l}\require{cancel}
5(0)-3(0)\lt10
\\\\
0\lt10
\text{ (TRUE)}
.\end{array}
Since the solution above ended with a $\text{
TRUE
}$ statement, then the testpoint is $\text{
part
}$ of the solution set.