Question

How do you graph `y<3x+5` and `y> -x+4`?

Answer 1

Graph and solve system of linear inequalities:
y < 3x + 5 (1)
y > -x + 4 (2)

Explanation:

First, graph Line (1) -> y = 3x + 5 by its 2 intercepts.
Make x = 0 --> y = 5. Make y = 0 --> `x = -5/3`.
The solution set of inequality (1) is the area below this line (1). Color or shade it.
Next, graph Line (2) -> y = - x + 4 by its 2 intercepts.
The solution set of inequality (2) is the area above the Line (2). Color or shade it.
The compound solution set is the commonly shared area.
graph{3x + 5 [-10, 10, -5, 5]}
graph{- x + 4 [-10, 10, -5, 5]}