Graphs 5
3 marks · NormalConsider the region defined by the inequalities and .
Describe how you would represent this region on a graph, stating whether each line should be solid or dashed.
For the line , give a suitable test point and check whether it lies inside the required region.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
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(a) Draw y = 2x + 3 as a solid line (since the inequality is ≤), and y = -x + 1 as a dashed line (since the inequality is >). Shade above y = -x + 1 and below or on y = 2x + 3.
(b) Test point (0,2): For y > -x + 1, 2 > -0 + 1 ⇒ 2 > 1 is true; so (0, 2) is in the region.
Show mark scheme and worked solution
Marking points
B1 (a) · 1 mark · States correct line style (solid for ≤, dashed for >)
B1 (a) · 1 mark · Correct method for deciding the region to shade
B1 (b) · 1 mark · Appropriate test point substituted correctly for y > -x + 1
Worked solution
a) Draw y = 2x + 3 as a solid line because ≤ includes the line. Draw y = -x + 1 as a dashed line because > does not include the line. The desired region is below or on y = 2x + 3 and above y = -x + 1.
b) Take test point (0, 2). For y > -x + 1: 2 > 1, so the point is in the required region.