To analyze the inequality 2x + y < 4, we first need to convert it into an equation to find out the boundary line. The equation corresponding to the inequality is:
2x + y = 4
Next, we determine the type of boundary line. Since the inequality is a strict one (<), the boundary line will be dashed. A dashed line indicates that points on the line do not satisfy the inequality.
Now, we need to find the shading for the graph. To do this, we can test a point that is not on the boundary line. A common choice is the origin, (0, 0). We substitute this point into the inequality:
2(0) + 0 < 4
This simplifies to:
0 < 4
This statement is true, so we shade the region that includes the origin. Thus, the area below the boundary line 2x + y = 4 will be shaded.
In summary, for the inequality 2x + y < 4:
- The boundary line is dashed.
- The region below the line will be shaded.