Question

How do you graph `2y ≤ x - 5`?

Answer 1

(1) `2y <= x - 5`
There are 2 ways:
1. Graph the line y = x/2 - 5/2 by slope-intercept form.
x = 0 y-intercept = -5/2
x = 2 -> y = 1 - 5/2 = -3/2
The solution set of the inequality (1) is the area below the Line. Color this area

1. By the standard form: `2y - x + 5 <= 0`
   x = 0 -> y = -5/2
   y = 0 -> x = 5
   Use the origin O as test point. Replace x = 0, y = 0 into inequality (1). It is 5 < 0. Untrue. Then the solution set of inequality (1) is the area below the Line. Color it.
   graph{2y - x + 5 = 0 [-10, 10, -5, 5]}