6. \( -x-2 y \geq 5 ;(-2,-3) \)

To solve the inequality \( -x - 2y \geq 5 \), let's first convert it into a more manageable form. Rearranging the terms gives us \( x + 2y \leq -5 \). Now, let's substitute the point \( (-2, -3) \) into the inequality: \(-(-2) - 2(-3) = 2 + 6 = 8\), which is not \( \geq 5 \). Thus, the point \( (-2, -3) \) does not satisfy the inequality. Now, if you were to graph the inequality, you'd shade the region that includes the line given by \( -x -2y = 5 \) in the opposite direction to where the point \( (-2,-3) \) sits. Remember, having clear boundaries makes understanding these concepts easier! If you're curious about graphing inequalities, a fantastic resource is online graphing tools like Desmos or GeoGebra. They let you visualize these inequalities and see how different points relate to the shaded area. You’ll have fun playing around with it, and maybe even discover new inequalities along the way!