Question

How do you find the graph of the inequality `y>=2x-3`?

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`

`y = (2 * 0) - 3`

`y = 0 - 3`

`y = -3` or `(0, -3)`

For `x = 2`

`y = (2 * 2) - 3`

`y = 4 - 3`

`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.
The boundary line will be solid because the inequality operator contains an "or equal to" clause.

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

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

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