Question

How do you graph the inequality `y<=-4x+12`?

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 = (-4 * 0) + 12`

`y = 0 + 12`

`y = 12` `(0, 12)`

For: `x = 3`

`y = (-4 * 3) + 12`

`y = -12 + 12`

`y = 0` `(3, 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.
The boundary line will be solid because the inequality operator contains an "or equal to" clause.

graph{(x^2+(y-12)^2-0.125)((x-3)^2+y^2-0.125)(4x+y-12)=0 [-30, 30, -15, 15]}

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

graph{(4x+y-12)<=0 [-30, 30, -15, 15]}