Question

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

Answer 1

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}