SOLUTION: graph the inequality 2x+5y>5

Algebra ->  Graphs -> SOLUTION: graph the inequality 2x+5y>5       Log On


   

Question 156326: graph the inequality
2x+5y>5




Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2x%2B5y%3E5 Start with the given inequality.


5y%3E5-2x Subtract 2x from both sides.


y%3E%285-2x%29%2F%285%29 Divide both sides by 5 to isolate y.


y%3E%285-2x%29%2F%285%29 Subtract x from both sides.


y%3E%28-2x%2B5%29%2F%285%29 Rearrange the terms.


y%3E%28-2x%29%2F%285%29%2B%285%29%2F%285%29 Break up the fraction.


y%3E-%282%2F5%29x%2B1 Reduce


So in order to graph 2x%2B5y%3E5, we need to graph y%3E-%282%2F5%29x%2B1. But first, we must graph the equation y=-%282%2F5%29x%2B1

graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C-%282%2F5%29x%2B1%29


Now plug in the test point (0,0) into y%3E-%282%2F5%29x%2B1


y%3E-%282%2F5%29x%2B1


0%3E-%282%2F5%290%2B1


0%3E1


Since the inequality is false, this means that we shade the entire region that does NOT contain (0,0). So this means that we shade everything above the line

Graph of y%3E-%282%2F5%29x%2B1 where the boundary (which should be a dotted line) is the equation y=-%282%2F5%29x%2B1 and the shaded region is in green.