How do you graph the inequality x - 2y ≤ 4?

Solution: 

The graph of the inequality is graphed as below:

The arrows indicate the area which satisfies the inequality x - 2y ≤ 4. The inequality also suggests that the points on line x - 2y = 4 are also included in the inequality.

The inequality region x - 2y ≤ 4 is ascertained by taking points on either side of the line and substituting in the inequality to verify.

1. Let us take a point (8, 0) which is below the line x - 2y = 4. Substituting x = 8 and y = 0 we get 8 - 2(0) ≤ 4 is incorrect hence the area below the line does not satisfy the inequality.
2. Let us take a point above the line (2, 1) and substitute in the inequality 2 - 2(1) ≤ 4 is correct. Hence the area above the line satisfies the inequality. Hence the area above is shaded with arrows

How do you graph the inequality x - 2y ≤ 4?

Summary:

the inequality x - 2y ≤ 4 is first graphed by first drawing the line x - 2y = 4 and then verifying which points on either side of the line satisfy the inequality. Accordingly, the relevant region is shaded as shown in the solution.