Question

graph the linear inequality
y < 2x + 4

use the graphing tool to graph the inequality.
click to enlarge graph

Explanation:

Step1: Identify boundary line

The inequality $y < 2x + 4$ has a boundary line $y = 2x + 4$. Since the inequality is $<$ (not $\leq$), the line will be dashed.

Step2: Find intercepts of boundary

• y-intercept: Set $x=0$, so $y=2(0)+4=4$. Point: $(0, 4)$
• x-intercept: Set $y=0$, so $0=2x+4 \implies x=-2$. Point: $(-2, 0)$

Step3: Determine shaded region

Test a point not on the line, e.g., $(0,0)$:
$0 < 2(0)+4 \implies 0 < 4$, which is true. So shade the region containing $(0,0)$ (below the dashed line).

Answer:

1. Draw a dashed line through points $(-2, 0)$ and $(0, 4)$ (representing $y=2x+4$).
2. Shade the entire region below this dashed line.