To graph the inequality \( y < -\frac{1}{2}x + 2 \), you can follow these steps:
-
Graph the Boundary Line: The first step is to graph the line \( y = -\frac{1}{2}x + 2 \). This line is the boundary of the inequality.
-
Find the y-intercept: When \( x = 0 \), \( y = 2 \). So, the point \( (0, 2) \) is on the line.
-
Find another point: To find another point, you can choose a value for \( x \). Let's choose \( x = 2 \): \[ y = -\frac{1}{2}(2) + 2 = -1 + 2 = 1. \] So, the point \( (2, 1) \) is also on the line.
-
Draw a dashed line through these points because the inequality is strict (\(<\)), which means the points on the line are not included.
-
-
Shade the Appropriate Region: Since the inequality is \( y < -\frac{1}{2}x + 2 \), you need to shade the region below the line. This shows all the points where \( y \) is less than the corresponding \( y \) value on the line.
-
Final Graph:
- The dashed line should slope downwards from left to right (negative slope) and you will shade the area below this line.
You can use graphing software or graphing paper to accurately represent the line and shading.
4 answers