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 $x+y=1$ using a solid line since it involves $\le$. (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: $x+y \le 1 \\0+0 \le 1 \\0 \le 1$ The statement is true. (3) The resulting statement in step (2) is true . This means that the solution set is the region that contain 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)