Question

algebra 2
1.5/2.1 graphing linear inequalities

• graph each, check to shade

1. 2x + y < 6

Explanation:

Step1: Convert to slope-intercept form

Rearrange the inequality to isolate $y$:
$2x + y < 6$
$y < -2x + 6$

Step2: Identify boundary line

The boundary is $y = -2x + 6$, a dashed line (since $<$ excludes equality).
Find intercepts:

• x-intercept: Set $y=0$: $0 = -2x + 6 \implies x=3$ (point $(3,0)$)
• y-intercept: Set $x=0$: $y=6$ (point $(0,6)$)

Step3: Test point for shading

Use the origin $(0,0)$:
$0 < -2(0) + 6 \implies 0 < 6$, which is true.

Answer:

1. Draw a dashed line connecting $(3,0)$ and $(0,6)$.
2. Shade the region below this dashed line (the side containing the origin $(0,0)$).