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Question: Which of the following system of linear inequalities to describe the graph.



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

Steps to derive

1 The y-intercept of Line 1 is 2 and slope is 23.
 [From the graph.]

2 The equation of Line 1 in slope-intercept form is y = 23x + 2
 [Substitute m = 23 and b = 2 in the equation y = mx + b.]

3 As Line 1 is a dashed line and the region above the line is shaded, the equation should be y > 23x + 2.
 [From the graph.]

4 The y-intercept of Line 2 is - 3 and slope is - 1.
 [From the graph.]

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

6 As Line 2 is a solid line and the region below the line is shaded, the inequality should be y ≤ - x - 3.
 [From the graph.]

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



Hence the right answer is Option C

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