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

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

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.

Sam believes (−4,−7) is a solution.

Answer 1

To check which pair is a solution of the equation \(1.5x - 2y = 8\), we need to substitute the given points into the equation and see if the left-hand side equals the right-hand side (8).

1. Peter believes (-4, 7) is a solution: \[ 1.5(-4) - 2(7) = -6 - 14 = -20 \quad (\text{not 8}) \]

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

3. Mary believes (4, -7) is a solution: \[ 1.5(4) - 2(-7) = 6 + 14 = 20 \quad (\text{not 8}) \]

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

The correct solution is Sam's belief that \((-4, -7)\) is a solution to the equation \(1.5x - 2y = 8\).