Question

How do you graph `3x+y<5`?

Answer 1

1. The first step is to treat the inequality as an equality.
   `3x + y = 5`

2. Then find coordinates that will create the border of the area that is represented by the inequality.
   (I usually rewrite the equation into slope-intercept form
   `y = -3x + 5` and graph that.)

3. Instead of graphing a straight line use a dotted line, since the original inequality `3x + y < 5` is less than rather then less than or equal.
   graph{3x + y < 5 [-10, 10, -5, 5]}

4. To decide which side of the line to graph, pick a coordinate pair on either side of dotted line. (I usually use `(0, 0)` ) and see if it makes the inequality true.
   ex. Is `(0, 0)` part of the solution set ?
   `3x + y < 5`
   `3(0) +0 < 5`
   `0 < 5` is a true statement so the left side of the dotted line should be shaded