Question

How do you graph the inequality: y<1/2x-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`

`y = (1/2 * 0) - 1`

`y = 0 - 1`

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

For: `x = 2`

`y = (1/2 * 2) - 1`

`y = 1 - 1`

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

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

Now, we can shade the right side of the line. And for the inequality we need to make the boundary line a dashed line because the inequality operator does not contains an "or equal to" clause.

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