Question

x - 2y ≥ 6
determine the following: slope, y - intercept, solid/dashed, shade above/below.
on paper, draw the graph.
select all 4 answers
□ m = 2
□ m = -5/2
□ m = 1/2
□ m = -3/2
□ m = 1
□ b = 2.5
□ b = -3
□ b = -5
□ b = -1
□ b = 0
□ solid
□ dashed
□ shade above
□ shade below

Explanation:

Step1: Rearrange to slope-intercept form

Start with $x - 2y \geq 6$. Isolate $y$:
$-2y \geq -x + 6$
Divide by $-2$ (reverse inequality):
$y \leq \frac{1}{2}x - 3$

Step2: Identify slope ($m$)

From $y = \frac{1}{2}x - 3$, slope is $\frac{1}{2}$.

Step3: Identify y-intercept ($b$)

From $y = \frac{1}{2}x - 3$, y-intercept is $-3$.

Step4: Determine line style

Inequality is $\geq$ (reversed to $\leq$), so line is solid.

Step5: Determine shading direction

Inequality is $y \leq \text{linear term}$, so shade below.

Answer:

• $\boldsymbol{m=1/2}$
• $\boldsymbol{b=-3}$
• $\boldsymbol{SOLID}$
• $\boldsymbol{SHADE BELOW}$