Question

How do you graph the inequality `2x - y + 3>0`?

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 + 3 = 0`
`-y + 3 = 0`
`color(red)(y) - y + 3 = color(red)(y)`
`0 + 3 = y`
`3 = y`
`y = 3` or `(0, 3)`

For: `x = 1`

`(2 * 1) - y + 3 = 0`
`2 - y + 3 = 0`
`-y + 2 + 3 = 0`
`-y + 5 = 0`
`color(red)(y) - y + 5 = color(red)(y)`
`0 + 5 = y`
`5 = y`
`y = 5` or `(1, 5)`

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-3)^2-0.125)((x-1)^2+(y-5)^2-0.125)(2x-y+3)=0 [-20, 20, -10, 10]}

To draw the inequality we will now make the boundary line dashed because the inequality operator does not contain an "or equal to" clause.

We can shade the right side of the line.

graph{(2x-y+3)>0 [-20, 20, -10, 10]}