How do you graph the inequality #2x-2y>=4# on the coordinate plane?

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Answer 1 · 2017-09-10T13:58:23

See a solution process below:

First, solve for two points as an equation instead of an inequality to find the boundary line for the inequality.

For: #x = 0#

#(2 * 0) - 2y = 4#

#0 - 2y = 4#

#-2y = 4#

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

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

For: #y = 0#

#2x - (2 * 0) = 4#

#2x - 0 = 4#

#2x = 4#

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

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

We can now graph the two points on the coordinate plane and draw a line through the points to mark the boundary of the inequality.

The boundary line will be solid because the inequality operator contains an "or equal to" clause.

graph{(x^2+(y+2)^2-0.125)((x-2)^2+y^2-0.125)(2x-2y-4)=0 [-20, 20, -10, 10]}

Now, we can shade the right side of the line.

graph{(2x-2y-4)>=0 [-20, 20, -10, 10]}