Question

How do you graph the inequality `y≥-1/4x+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 = (-1/4 * 0) + 3`

`y = 0 + 3`

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

For: `x = 4`

`y = (-1/4 * 4) + 3`

`y = -1 + 3`

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

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-4)^2+(y-2)^2-0.125)((1/4)x+y-3)=0 [-20, 20, -10, 10]}

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

graph{((1/4)x+y-3) >= 0 [-20, 20, -10, 10]}}