Question

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

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 = (1/2 xx 0) + 2`

`y = 0 + 2`

`y = 2` or `(0, 2)`

For: `x = 2`

`y = (1/2 xx 2) + 2`

`y = 2/2 + 2`

`y = 1 + 2`

`y = 3` or `(2, 3)`

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-2)^2-0.04)((x-2)^2+(y-3)^2-0.04)(-0.5x+y-2)=0 [-10, 10, -5, 5]}

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

However, we must change the boundary line to a dashed line because the inequality operator does not contain an "or equal to" clause.

graph{(-0.5x+y-2) < 0 [-10, 10, -5, 5]}