SOLUTION: Please help me with the following question: Graph each inequality x/5 + y/4 <1

Algebra ->  Inequalities -> SOLUTION: Please help me with the following question: Graph each inequality x/5 + y/4 <1      Log On


   

Question 146526This question is from textbook
: Please help me with the following question: Graph each inequality x/5 + y/4 <1 This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%2F5%2By%2F4%3C1 Start with the given inequality.


x%2F5%2By%2F4=1 Replace the inequality sign with an equals sign.


20%28x%2F5%2By%2F4%29=20%281%29 Multiply both sides by the LCD 20 to clear any fractions.


4x%2B5y=20 Distribute and multiply.


5y=20-4x Subtract 4x from both sides.


y=%2820-4x%29%2F%285%29 Divide both sides by 5 to isolate y.


y=-%284%2F5%29x%2B4 Rearrange the terms.


So in order to plot x%2F5%2By%2F4%3C1 or y%3C-%284%2F5%29x%2B4 (which is the same thing), we need to plot the equation y=-%284%2F5%29x%2B4 first.
(note: if you need help with graphing, check out this solver)


+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%284%2F5%29x%2B4%29+ Graph of y=-%284%2F5%29x%2B4


Now plug in a test point (0,0) into the inequality y%3C-%284%2F5%29x%2B4


y%3C-%284%2F5%29x%2B4 Start with the given inequality.


0%3C-%284%2F5%29%2A%280%29%2B4 Plug in x=0 and y=0


0%3C4 Evaluate and simplify.


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


In other words, we simply shade the entire region that is below the line.


Graph of y%3C-%284%2F5%29x%2B4 with the shaded region in green