SOLUTION: graph the inequality in the coordinate plane 2x-4y_<16

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Question 147754This question is from textbook
: graph the inequality in the coordinate plane 2x-4y_<16 This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

2x-4y%3C=16 Start with the given inequality.


2x-4y=16 Replace the inequality sign with an equals sign.


-4y=16-2x Subtract 2x from both sides.


y=%2816-2x%29%2F%28-4%29 Divide both sides by -4 to isolate y.


y=%281%2F2%29x-4 Simplify.


So in order to plot 2x-4y%3C=16 or y%3E=%281%2F2%29x-4 (which is the same thing), we need to plot the equation y=%281%2F2%29x-4 first.
(note: if you need help with graphing, check out this solver)


+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%281%2F2%29x-4%29+ Graph of y=%281%2F2%29x-4


Now plug in a test point (0,0) into the inequality y%3E=%281%2F2%29x-4


y%3E=%281%2F2%29x-4 Start with the given inequality.


0%3E=%281%2F2%29%2A%280%29-4 Plug in x=0 and y=0


0%3E=-4 Evaluate and simplify.


Since the inequality is true, this means that we shade the entire region that contains the point (0,0)


In other words, we simply shade the entire region that is above the line.


Graph of y%3E=%281%2F2%29x-4 with the shaded region in green