Question

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

Answer 1

See a solution process below:

Explanation:

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]}