Rewrite the inequality as
[tex]y > -2x+4[/tex]
We can compare this expression to the function
[tex]y=-2x+4[/tex]
The inequality states that we want to consider all the point whose y coordinates are greater than the ones of the points that lay on the graph.
So, we can graph the inequality in two steps:
- Graph the line [tex]y=-2x+4[/tex]
- Consider all the point above the graph (greater y values means "higher")
Since the function [tex]y=-2x+4[/tex] is a line (because it is a first-degree polynomial), you can graph it by simply sampling two points: if for example we choose x=0 and x=1, the correspondent y values are
[tex]x=0 \implies y = -2\cdot 0+4 = 4,\quad x=1\implies y = -2\cdot 1+4 = 2[/tex]
So, the line passes through the points (0,4) and (-1,2). Connect them and you have the graph of the line.
