How do you graph the inequality #x+2y≥4#?

1 Answer
Aug 15, 2017

See a solution process below:

Explanation:

First, find two points on the line if you change the inequality to an equation.

For #x = 0#: #0 + 2y = 4#

#2y = 4#

#(2y)/color(red)(2) = 4/color(red)(2)#

#y = 2# or #(0, 2)#

For #y = 0#: #x + 0 = 4#

#x = 4# or #(4, 0)#

We can plot these two points and draw a line through them to get the border of the inequality:

graph{(x^2+(y-2)^2-0.075)((x-4)^2+y^2-0.075)(x+2y-4)=0}

The line will be solid because the inequality operator has a "or equal to" clause in it. We can now shade the area to the right of the line because the inequality has a "great than" clause in it.

graph{(x+2y-4)>=0}