Question

How do you graph `3x - 2y ≥ 6`?

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`

`(3 * 0) - 2y = 6`

`0 - 2y = 6`

`-2y = 6`

`(-2y)/color(red)(-2) = 6/color(red)(-2)`

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

For: `y = 0`

`3x - (2 xx 0) = 6`

`3x - 0 = 6`

`3x = 6`

`(3x)/color(red)(3) = 6/color(red)(3)`

`x = 2` 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.
The boundary line will be solid because the inequality operator contains an "or equal to" clause.

graph{(x^2+(y+3)^2-0.04)((x-2)^2+y^2-0.04)(3x-2y-6)=0 [-10, 10, -5, 5]}

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

graph{(3x-2y-6) >= 0 [-10, 10, -5, 5]}