Question

How do you graph `3x + y < 4`?

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) + y = 4`

`0 + y = 4`

`y = 4` or `(0, 4)`

For: `x = 2`

`(3 * 2) + y = 4`

`6 + y = 4`

`-color(red)(6) + 6 + y = -color(red)(6) + 4`

`0 + y = -2`

`y = -2` or `(2, -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.

graph{(x^2+(y-4)^2-0.05)((x-2)^2+(y+2)^2-0.05)(3x+y-4)=0 [-10, 10, -5, 5]}

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

graph{(3x+y-4) < 0 [-10, 10, -5, 5]}