\( R = y \geq 2 x + 1 \)

The inequality \( R = y \geq 2x + 1 \) describes a region in the Cartesian coordinate system. Let's break it down: 1. **Understanding the Equation**: The equation \( y = 2x + 1 \) represents a straight line with a slope of 2 and a y-intercept of 1. This means that for every unit increase in \( x \), \( y \) increases by 2 units. 2. **Graphing the Line**: To graph the line, you can plot the y-intercept (0, 1) and another point. For example, when \( x = 1 \): \[ y = 2(1) + 1 = 3 \] So, the point (1, 3) is also on the line. You can draw a straight line through these points. 3. **Shading the Region**: The inequality \( y \geq 2x + 1 \) indicates that we are interested in the region above (and including) the line \( y = 2x + 1 \). This means you will shade the area above the line. 4. **Boundary Line**: Since the inequality is "greater than or equal to," the line itself is included in the solution set. Therefore, you would draw the line as a solid line. In summary, the region \( R \) consists of all points \((x, y)\) in the coordinate plane that lie on or above the line \( y = 2x + 1 \).