SOLUTION: If anyone can help I will be eternally grateful and interested in if you are a private tutor. How do you graph 4x + y is greater than or equal to 4

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Question 88826: If anyone can help I will be eternally grateful and interested in if you are a private tutor. How do you graph 4x + y is greater than or equal to 4
Found 2 solutions by checkley75, jim_thompson5910:
Answer by checkley75(3666) About Me  (Show Source):
You can put this solution on YOUR website!
4X+Y=4 OR Y=-4X+4 GRAPHED THIS LINE IS: +graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+y++=+-4x+%2B4%29+ (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, y = -4x +4).
Now you need to darken the area to the right & above this line for all values > or = 4.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
In order to graph 4x%2By%3E=4, 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, (just make sure the point doesn't lie on the line) but this point is the easiest to work with. Now evaluate the inequality 4x%2By%3E=4 with the test point

Substitute (0,0) into the inequality
4%280%29%2B%280%29%3E=4 Plug in x=0 and y=0
0%3E=4 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 (note: for some reason, this image does not display in Internet Explorer. So I would recommend the use of Firefox to see this image.)
Graph of 4x%2By%3E=4 with the boundary (which is the line 4x%2By=4 in red) and the shaded region (in green)