Question

2. Graph x + 3y ≤ 6, indicating the solution set with crosshatching or shading. Explain how you determined where to draw the line and shade the area that represents the solution set.

Answer 1

You graph the line x + 3y = 6, which is y = (6 -x)/3. You should not need help doing this.
Then we take any point we can think of that satisfies x + 3y ≤ 6. Let's take (0,0) for example. We know that 0 + 0 <= 6. We plot (0, 0) and see if it's above or below the line. We notice that it's below the line, telling us that we shade everything below the equation.
Since it's ≤, the line should be solid to indicate that points on the line are included.