The math teacher asked his students to determine a solution for 1.5x−2y=8. Which solution below is the correct one?(1 point)

Question

Responses

Fiona believes (4,7) is a solution.
Fiona believes left parenthesis 4 comma 7 right parenthesis is a solution.

Mary believes (4,−7) is a solution.
Mary believes left parenthesis 4 comma negative 7 right parenthesis is a solution.

Peter believes (−4,7) is a solution.
Peter believes left parenthesis negative 4 comma 7 right parenthesis is a solution.

Sam believes (−4,−7) is a solution.

Answer 1

To determine which of these points is a solution to the equation \(1.5x - 2y = 8\), we need to substitute each pair of values into the equation.

1. Fiona's solution: \((4, 7)\) \[ 1.5(4) - 2(7) = 6 - 14 = -8 \quad \text{(not a solution)} \]

2. Mary's solution: \((4, -7)\) \[ 1.5(4) - 2(-7) = 6 + 14 = 20 \quad \text{(not a solution)} \]

3. Peter's solution: \((-4, 7)\) \[ 1.5(-4) - 2(7) = -6 - 14 = -20 \quad \text{(not a solution)} \]

4. Sam's solution: \((-4, -7)\) \[ 1.5(-4) - 2(-7) = -6 + 14 = 8 \quad \text{(solution)} \]

The only point that satisfies the equation \(1.5x - 2y = 8\) is Sam's solution: \((-4, -7)\).