Answer
Refer to the image below for the graph.
Work Step by Step
To graph the given inequality, do the following:
(1) Graph the boundary line $3x+y=1$.
(refer to the attached image below for the graph)
(2) Choose a test point that is not on the boundary line. Substitute the x and y values of the test point into the inequality.
Let $(2,0)$ be the test point.
$3x+y\le 1
\\3(2) + 0 \le 1
\\6+0 \le 1
\\6 \le 1$
This statement is false therefore the solution to the inequality is the other half-plane on the other side of the boundary line. Shade that region to complete the graph.
(refer to the attached image in the answer part for the graph)