Question

graph the inequality on a plane. (click to shade a region below or above the line).
$4x - 2y < -8$
toggle lines solidity

Explanation:

Step1: Rearrange to slope-intercept form

Start with the given inequality:
$4x - 2y < -8$
Subtract $4x$ from both sides:
$-2y < -4x - 8$

Step2: Isolate y (reverse inequality)

Divide all terms by $-2$, reversing the inequality sign:
$y > 2x + 4$

Step3: Identify line type

Since the inequality is $>$ (not $\geq$), use a dashed line for $y=2x+4$ (already shown in the graph).

Step4: Determine shaded region

Test a point not on the line, e.g., $(0,0)$:
$0 > 2(0) + 4$ → $0 > 4$, which is false. So shade the region above the dashed line (where the inequality holds true).

Answer:

1. The boundary line is the dashed line $y=2x+4$ (already correctly displayed).
2. Shade the region above this dashed line to represent the solution set of $4x - 2y < -8$.