How do you graph #y>=3-x#?

1 Answer
Feb 4, 2015

Solving linear inequalities in two variable is very easy when you can write is as #y\ge f(x)# (or #y \le f(x)#).

In these cases, in fact, the graph of #f(x)# represents the points where #y=f(x)# holds. To solve #y\ge f(x)# you'll need to consider all the points "above" the graph, and vice versa for #y \le f(x)#.

In your case, #f(x)=3-x#, which is a line. A line can be graphed once two of its points are known. You can choose two easy points by setting #x=0# (obtaining #y=3#), and #x=3# (obtaining #y=0#).

So, the points #(0,3)# and #(3,0)# belong to the line. Connect them to find the graph of the line, and consider all the points above the line to solve the inequality.

Here's the graph: graph{y \ge 3-x [-10, 10, -5, 5]}