SOLUTION: solve and graph the following inequality 4x+y greater than 4

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Question 87377: solve and graph the following inequality
4x+y greater than 4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
In order to graph 4x%2By%3E4, we need to graph the equation 4x%2By=4 (just replace the inequality sign with an equal sign).
So lets graph the line 4x%2By=4 (note: if you need help with graphing, check out this solver)

+graph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C+-4x%2B4%29+ graph of 4x%2By=4
Now lets pick a test point, say (0,0) (any point will work, but this point is the easiest to work with), and evaluate the inequality 4x%2By%3E4

Substitute (0,0) into the inequality
4%280%29%2B%280%29%3E4 Plug in x=0 and y=0
0%3E4 Simplify
Since this inequality is not true, we do not shade the entire region that contains (0,0). So this means we shade the region that is on the opposite side of the line
Graph of 4x%2By%3E4 with the boundary (which is the line 4x%2By=4 in red) and the shaded region (in green)
(note: since the inequality contains a greater-than sign, this means the boundary is excluded. This means the solid red line is really a dashed line)