SOLUTION: I was wondering if someone could explain how to shade linear equalities when you graph them. I know how to graph, I'm just confused on where to shade. 3y + x > 4

Algebra ->  Linear-equations -> SOLUTION: I was wondering if someone could explain how to shade linear equalities when you graph them. I know how to graph, I'm just confused on where to shade. 3y + x > 4      Log On


   

Question 150538: I was wondering if someone could explain how to shade linear equalities when you graph them. I know how to graph, I'm just confused on where to shade.
3y + x > 4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

3y%2Bx%3E4 Start with the given inequality.


3y%3E4-x Subtract x from both sides.


y%3E%284-x%29%2F%283%29 Divide both sides by 3 to isolate y.


y%3E%284%29%2F3-%28x%29%2F%283%29 Break up the fraction.


y%3E-%281%2F3%29x%2B4%2F3 Rearrange the terms.


So in order to plot 3y%2Bx%3E4 or y%3E-%281%2F3%29x%2B4%2F3 (which is the same thing), we need to plot the equation y=-%281%2F3%29x%2B4%2F3 first.


+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%281%2F3%29x%2B4%2F3%29+ Graph of y=-%281%2F3%29x%2B4%2F3


Now plug in a test point (0,0) into the inequality y%3E-%281%2F3%29x%2B4%2F3


y%3E-%281%2F3%29x%2B4%2F3 Start with the given inequality.


0%3E-%281%2F3%29%2A%280%29%2B4%2F3 Plug in x=0 and y=0


0%3E4%2F3 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-%281%2F3%29x%2B4%2F3 (which is also 3y%2Bx%3E4 )with the shaded region in green


Note: Since the inequality has a greater than sign ">", this means that the red boundary line should be dotted since we are not including this line with the solution set.