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 $x-y=7$. (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 $(0,0)$ be the test point. $x-y\ge 7 \\0-0\ge 7 \\0 \ge 7$ 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)