Question

How do you graph `y<4x - 6` and `y>4x + 2`?

Answer 1

Graph the system
y < 4x - 6 (1)
y > 4x + 2 (2)

Explanation:

First graph the line y1 = 4x - 6 by its 2 intercepts.
Make x = 0 -> y = -6. Make y = 0 ->`x = 6/4 = 3/2`
The solution set of the inequality (1) is the area below line y1. Shade or color it.
Next, graph the line y2 = 4x + 2 by its 2 intercepts.
The solution set of (2) is the area above the line y2. Color or shade it.
The compound solution set of the system is the commonly shared area.
Note, the 2 lines are parallel because they have same slope (4). The band between the 2 lines is the compound solution set.
graph{4x - 6 [-10, 10, -5, 5]}
graph{4x + 2 [-10, 10, -5, 5]}