Question

How do you graph the inequality `2x + y > 1`?

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 = 1`

`0 + y = 1`

`y = 1` or `(0, 1)`

For: `x = 1`

`(2 * 1) + y = 1`

`2 + y = 1`

`-color(red)(2) + 2 + y = -color(red)(2) + 1`

`0 + y = -1`

`y = -1` or `(1, -1)`

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.

graph{(x^2+(y-1)^2-0.025)((x-1)^2+(y+1)^2-0.025)(2x+y-1)=0 [-10, 10, -5, 5]}

Now, we can shade the right side of the line. The boundary line needs to be changed to a dashed line because the inequality operator does not contain an "or equal to" clause.

graph{(2x+y-1) > 0 [-10, 10, -5, 5]}