Question

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

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) + y = 4`

`0 + y = 4`

`y = 4`

`y = 4` or `(0, )`

For: `x = 2`

`(2 * 2) + y = 4`

`4 + y = 4`

`-color(red)(4) + 4 + y = -color(red)(4) + 4`

`0 + y = 0`

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

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

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