Question

choose all that correctly graph the given inequality.
a
$y \geq -6x - 2$
b
$y \leq 3x + 2$
c
$y \geq \frac{1}{2}x + 1$
d
$y \leq \frac{1}{5}x - 2$

Explanation:

Step1: Analyze Option A

First, identify the boundary line $y=-6x-2$. The y-intercept is $-2$, slope is $-6$, matching the graph. The inequality $y\geq-6x-2$ means we shade above the line, which matches the graph.

Step2: Analyze Option B

Boundary line $y=3x+2$ has y-intercept $2$, slope $3$, matching the graph. The inequality $y\leq3x+2$ means we shade below the line, but the graph shades above, so this is incorrect.

Step3: Analyze Option C

Boundary line $y=\frac{1}{2}x+1$ has y-intercept $1$, slope $\frac{1}{2}$, matching the graph. The inequality $y\geq\frac{1}{2}x+1$ means we shade above the line, which matches the graph.

Step4: Analyze Option D

Boundary line $y=\frac{1}{5}x-2$ has y-intercept $-2$, slope $\frac{1}{5}$, matching the graph. The inequality $y\leq\frac{1}{5}x-2$ means we shade below the line, which matches the graph.

Answer:

A. Graph of $y\geq -6x - 2$
C. Graph of $y\geq \frac{1}{2}x + 1$
D. Graph of $y\leq \frac{1}{5}x - 2$