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Question: Write a system of linear inequalities to describe the graph.



A ) y > x + 3; y < 23x + 2
B ) y < x + 2; y > 23x - 2
C ) y > x + 1; y ≤ 23x + 2
D ) y < x + 3; y > 23x + 2

Steps to derive

1 The y-intercept of Line 1 is 3 and slope is 1.
 [From the graph.]

2 The equation of Line 1 in slope-intercept form is y = x + 3.
 [Substitute m = 1 and b = 3 in the equation y = mx + b.]

3 As Line 1 is a dashed line and the region below the line is shaded, the equation should be y < x + 3.
 [From the graph.]

4 The y-intercept of Line 2 is 2 and slope is 23.
 [From the graph.]

5 The equation of Line 2 in slope-intercept form is y = 23x + 2.
 [Substitute m = 23and b = 2 in the equation y = mx + b.]

6 As Line 2 is a dashed line and the region above the line is shaded, the equation should be y > 23x + 2.
 [From the graph.]

7 So, the system of inequalities is y < x + 3 and y > 23x + 2.



Hence the right answer is Option D

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