SOLUTION: Graph the inequality: y < (1/2)x + 1

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Question 134196: Graph the inequality: y < (1/2)x + 1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First graph y+=+%281%2F2%29x+%2B+1

+graph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C+%281%2F2%29x%2B1%29+ graph of y=%281%2F2%29x+%2B+1

Now lets pick a test point, say (0,0). Any point will work, (just make sure the point doesn't lie on the line) but this point is the easiest to work with. Now evaluate the inequality -x%2B2y%3C2 with the test point

Substitute (0,0) into the inequality

0%3C%281%2F2%29%280%29+%2B+1 Plug in x=0 and y=0

0%3C1 Simplify



(note: for some reason, some of the following images do not display correctly in Internet Explorer. So I recommend the use of Firefox to see these images.)


Since this inequality is true, we simply shade the entire region that contains (0,0)
Graph of y%3C%281%2F2%29x+%2B+1 with the boundary (which is the line y=%281%2F2%29x+%2B+1 in red) and the shaded region (in green)
(note: since the inequality contains a less-than sign, this means the boundary is excluded. This means the solid red line is really a dashed line)