SOLUTION: Graph the equality on a plane. 3x+4y is greater than or = to 12

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Question 146775: Graph the equality on a plane.
3x+4y is greater than or = to 12
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

3x%2B4y%3E=12 Start with the given inequality.


3x%2B4y=12 Replace the inequality sign with an equals sign.


4y=12-3x Subtract 3x from both sides.


y=%2812-3x%29%2F%284%29 Divide both sides by 4 to isolate y.


y=-%283%2F4%29x%2B3 Rearrange the terms.


So in order to plot 3x%2B4y%3E=12 or y%3E=-%283%2F4%29x%2B3 (which is the same thing), we need to plot the equation y=-%283%2F4%29x%2B3 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-%283%2F4%29x%2B3%29+ Graph of y=-%283%2F4%29x%2B3


Now plug in a test point (0,0) into the inequality y%3E=-%283%2F4%29x%2B3


y%3E=-%283%2F4%29x%2B3 Start with the given inequality.


0%3E=-%283%2F4%29%2A%280%29%2B3 Plug in x=0 and y=0


0%3E=3 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=-%283%2F4%29x%2B3 with the shaded region in green