Which linear inequality is graphed with y < x + 2 to create the given solution set?

The linear inequality that corresponds to the solution set illustrated in the graph is y < x + 2.

To understand why, let’s break down the components:

1. Understanding the Inequality: The expression ‘y < x + 2' signifies that for any point in the solution set, the y-value must always be less than the y-value of the line defined by 'y = x + 2'.
2. Graphing the Boundary Line: The boundary line for this inequality is obtained by replacing the inequality with an equality: y = x + 2. This line has a slope of 1 and a y-intercept of 2.
3. Shading the Correct Region: Since the inequality is ‘less than’ (<), we shade the area below this line. This shading represents all the points where y is less than 'x + 2'.

Thus, the solution set includes all points in the region below the line, confirming that ‘y < x + 2' accurately represents the graphed inequality.