Refer to the image below for the graph.
Work Step by Step
To graph the given inequality, perform the following steps: (1) Graph the boundary line $x-3y=3$ using dashed line since it involves $\lt$. (refer to the image below for the graph) (2) Use the test point $(0, 0)$. Substitute the x and y values of this point into the given inequality to obtain: $x-3y \lt 3 \\0-3(0) \lt 3 \\0 \lt 3$ The statement is true. (3) The resulting statement in step (2) is true. This means that the solution set is the region that contains the test point $(0, 0)$. To complete the graph, shade the region that contains $(0, 0)$. (refer to the attached image in the answer part above for the graph)