91Ó°ÊÓ

To sketch the region corresponding to the given inequality, first, we need to rewrite it as an equation. This is done by replacing the inequality symbol (≤) with an equals sign (=): \[ \frac{3x}{4} - \frac{y}{4} = 1 \] Now, to graph this line, it's helpful to get it in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. Solve for y: \[ -\frac{y}{4} = -\frac{3x}{4} + 1 \] \[ y = 3x - 4 \] The slope is 3, and the y-intercept is -4. Now, test a point on the other side (non-shaded side) of the line to verify if it satisfies the inequality. If it does, then we will shade this side of the line. Let's pick the point (0,0): \[ \frac{3(0)}{4}-\frac{(0)}{4}\leq1 \] \[ 0\leq1 \] Since the inequality holds true, we will shade the side of the line opposite the y-intercept.

A region is bounded if it is enclosed by lines or curves and unbounded if it extends indefinitely. In this case, there is nothing stopping the shading from extending forever in one direction, so the region is unbounded.

Corner points occur at the intersection of boundary lines (where lines change from solid to dashed). However, in this case, there is only one boundary line (the line y = 3x - 4). Since there is no intersection of multiple boundary lines in this problem, there are no corner points associated with the inequality. So, the final answer is: 1. The region corresponding to the inequality is the area above the line y = 3x - 4. 2. The region is unbounded. 3. There are no corner points for the given inequality.