Question

How do you graph the inequality `-2 x + y> -5`?

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 = -5`

`0 + y = -5`

`y = -5` or `(0, -5)`

For: `x = 2`

`(-2 * 2) + y = -5`

`-4 + y = -5`

`color(red)(4) - 4 + y = color(red)(4) - 5`

`0 + y = -1`

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

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

We also need to change the boundary line to a dashed line because the inequality operator does not contain an "or equal to" clause.

graph{(-2x+y+5) > 0 [-20, 20, -10, 10]}