SOLUTION: graph the inequality on a plane 3y-4x>12

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Question 146656: graph the inequality on a plane
3y-4x>12
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

3y-4x%3E12 Start with the given inequality.


3y-4x=12 Replace the inequality sign with an equals sign.


3y=12%2B4x Add 4x to both sides.


y=%2812%2B4x%29%2F%283%29 Divide both sides by 3 to isolate y.


y=%284%2F3%29x%2B4 Rearrange the terms.


So in order to plot 3y-4x%3E12 or y%3E%284%2F3%29x%2B4 (which is the same thing), we need to plot the equation y=%284%2F3%29x%2B4 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%284%2F3%29x%2B4%29+ Graph of y=%284%2F3%29x%2B4


Now plug in a test point (0,0) into the inequality y%3E%284%2F3%29x%2B4


y%3E%284%2F3%29x%2B4 Start with the given inequality.


0%3E%284%2F3%29%2A%280%29%2B4 Plug in x=0 and y=0


0%3E4 Evaluate and simplify.


Since the inequality is false, this means that we shade the entire region that does NOT contain the point (0,0)


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


Graph of y%3E%284%2F3%29x%2B4 with the shaded region in green