SOLUTION: Graph the inequality on a plane {{{3x+4y<=12}}}

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Question 145959: Graph the inequality on a plane
3x%2B4y%3C=12
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

3x%2B4y%3C12 Start with the 1st inequality


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


y=-%283%2F4%29x%2B3 Solve for y


So in order to plot y%3C-%283%2F4%29x%2B3, we need to plot the equation y=-%283%2F4%29x%2B3 first


+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%3C-%283%2F4%29x%2B3


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


0%3C3 Evaluate and simplify


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


Graph of y%3C-%283%2F4%29x%2B3 with the shaded region in green