Question: Which system of linear inequalities describes the graph?
A ) y ≥ - 32x - 3; y ≤ - x + 3
B ) y ≥ 32x + 3; y > - x + 3
C ) y ≤ 32x + 3; y ≥ - x - 3
D ) y ≤ 32x + 3; y < - x - 3
Steps to derive
1 The y-intercept of the Line 1 is 3 and the slope is 32.
[From the graph.]
2 The equation of Line 1 in slope-intercept form is y = 32x + 3.
[Substitute m = 32 and b = 3 in the equation y = mx + b.]
3 As Line 1 is a solid line and the region above the line is shaded, the equation should be y ≥ 32x + 3.
[From the graph.]
4 The y-intercept of Line 2 is 3 and the slope is - 1.
[From the graph.]
5 The equation of Line 2 in 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 dashed line and the region above the line is shaded, the inequality should be y > - x + 3.
[From the graph.]
7 So, the system of linear inequalities is y ≥ 32x + 3 and y > - x + 3.
Hence the right answer is Option B
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