Question

How do you graph 2x + y > 4

Answer 1

Rewrite the inequality as

$y > -2x+4$

We can compare this expression to the function

$y=-2x+4$

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:

1. Graph the line $y=-2x+4$
2. Consider all the point above the graph (greater y values means "higher")

Since the function $y=-2x+4$ 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

$x=0 \implies y = -2\cdot 0+4 = 4,\quad x=1\implies y = -2\cdot 1+4 = 2$

So, the line passes through the points (0,4) and (-1,2). Connect them and you have the graph of the line.