See graph and explanations.
Work Step by Step
Step 1. Graph the line $x-2y\gt10$. Since the inequality does not include an equal sign, make this line dashed. Step 2. Using a test point away from the line, such as $(0,0)$, we have $0\gt10$, which is not true. Thus, the other side which does not include this test point should be shaded as shown in the figure.