Question

the graph of $y \leq \frac{3}{2}x - \frac{1}{2}$ is shown. which of the following ordered pairs $(x, y)$ satisfies the inequality? choose 1 answer: \\(\boldsymbol{\text{a}}\\) \\((-3, -4)\\) \\(\boldsymbol{\text{b}}\\) \\((0, 1)\\) \\(\boldsymbol{\text{c}}\\) \\((2, 0)\\) \\(\boldsymbol{\text{d}}\\) \\((3, 5)\\)

Explanation:

Step1: Test Option A (-3,-4)

Substitute $x=-3, y=-4$ into $\displaystyle y \leq \frac{3}{2}x - \frac{1}{2}$:
$\displaystyle -4 \leq \frac{3}{2}(-3) - \frac{1}{2} = \frac{-9 -1}{2} = -5$
$-4 \leq -5$ is false.

Step2: Test Option B (0,1)

Substitute $x=0, y=1$ into $\displaystyle y \leq \frac{3}{2}x - \frac{1}{2}$:
$\displaystyle 1 \leq \frac{3}{2}(0) - \frac{1}{2} = -\frac{1}{2}$
$1 \leq -\frac{1}{2}$ is false.

Step3: Test Option C (2,0)

Substitute $x=2, y=0$ into $\displaystyle y \leq \frac{3}{2}x - \frac{1}{2}$:
$\displaystyle 0 \leq \frac{3}{2}(2) - \frac{1}{2} = 3 - \frac{1}{2} = \frac{5}{2}$
$0 \leq \frac{5}{2}$ is true.

Step4: Verify Option D (3,5)

Substitute $x=3, y=5$ into $\displaystyle y \leq \frac{3}{2}x - \frac{1}{2}$:
$\displaystyle 5 \leq \frac{3}{2}(3) - \frac{1}{2} = \frac{9 -1}{2} = 4$
$5 \leq 4$ is false.

Answer:

C. (2, 0)