Question

2 which ordered pair is in the solution set of \\(y > \frac{3}{2}x - 1\\)?

f \\((-2,-4)\\)
g \\((-4,2)\\)
h \\((2,2)\\)
j \\((2,0)\\)

Explanation:

Identify the inequality and options

The given inequality is:

$$y > \frac{3}{2}x - 1$$

The options to test are:

• \(F: (-2, -4)\)
• \(G: (-4, 2)\)
• \(H: (2, 2)\)
• \(J: (2, 0)\)

Test each ordered pair

Substitute each coordinate pair \((x, y)\) into the inequality:

• For \(F(-2, -4)\):

$$-4 > \frac{3}{2}(-2) - 1 \implies -4 > -3 - 1 \implies -4 > -4 \quad (\text{False})$$

• For \(G(-4, 2)\):

$$2 > \frac{3}{2}(-4) - 1 \implies 2 > -6 - 1 \implies 2 > -7 \quad (\text{True})$$

• For \(H(2, 2)\):

$$2 > \frac{3}{2}(2) - 1 \implies 2 > 3 - 1 \implies 2 > 2 \quad (\text{False})$$

• For \(J(2, 0)\):

$$0 > \frac{3}{2}(2) - 1 \implies 0 > 3 - 1 \implies 0 > 2 \quad (\text{False})$$

Determine the correct option

The only ordered pair that satisfies the inequality is \(G(-4, 2)\).

Answer:

• F \((-2,-4)\)
• G \((-4,2)\) (Correct answer)
• H \((2,2)\)
• J \((2,0)\)