11. \( y>\frac{3}{2} x-4 \)

The inequality \( y > \frac{3}{2} x - 4 \) represents a region in the coordinate plane. To understand this inequality better, we can analyze it step by step. 1. **Identify the boundary line**: The equation of the line corresponding to the inequality is \( y = \frac{3}{2} x - 4 \). This line has a slope of \( \frac{3}{2} \) and a y-intercept of \(-4\). 2. **Graph the boundary line**: - To graph the line, you can plot the y-intercept at (0, -4). - From there, use the slope to find another point. For example, from (0, -4), you can move up 3 units and right 2 units to reach the point (2, -1). - Draw a dashed line through these points because the inequality is strict (i.e., \( y > \) rather than \( y \geq \)). 3. **Determine the region**: Since the inequality is \( y > \frac{3}{2} x - 4 \), you will shade the region above the line. This indicates all the points (x, y) that satisfy the inequality. 4. **Test a point**: To confirm which side to shade, you can test a point not on the line. A common choice is the origin (0, 0): \[ 0 > \frac{3}{2}(0) - 4 \implies 0 > -4 \] This is true, so the region that includes the origin (the area above the line) is the correct region to shade. In summary, the solution to the inequality \( y > \frac{3}{2} x - 4 \) is the area above the dashed line \( y = \frac{3}{2} x - 4 \) in the coordinate plane.