Question

How do you graph the inequality `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 * 0) = 6`

`3x + 0 = 6`

`3x = 6`

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

graph{(x^2+(y-3)^2-0.125)((x-2)^2+ y^2-0.125)(3x+2y-6)=0 [-20, 20, -10, 10]}

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

graph{(3x+2y-6) < 0 [-20, 20, -10, 10]}