Question

text description for graph
a. $y > x$
$y < 2$
b. $y > x$
$y > 2$
c. $y < x$
$y > 2$
d. $y < x$
$y < 2$

Explanation:

Step1: Analyze the line \( y = x \)

The line \( y = x \) has a slope of 1 and passes through the origin. The shaded region is above this line, so the inequality related to this line is \( y > x \) (since the line is dashed, it's a strict inequality).

Step2: Analyze the horizontal line

The horizontal dashed line is \( y = 2 \). The shaded region is above this line, so the inequality related to this line is \( y > 2 \) (again, dashed line means strict inequality).

Step3: Match with options

Looking at the options, option B has \( y > x \) and \( y > 2 \), which matches the analysis of the two inequalities from the graph.

Answer:

B. \( y > x \)
\( y > 2 \)