To determine if any of the proposed points \((x, y)\) are solutions to the equation \(1.5x - 2y = 8\), we can substitute each pair of values into the equation and see if the equation holds true.
-
Fiona believes (4, 7) is a solution: \[ 1.5(4) - 2(7) = 6 - 14 = -8 \quad (\text{not a solution}) \]
-
Mary believes (4, -7) is a solution: \[ 1.5(4) - 2(-7) = 6 + 14 = 20 \quad (\text{not a solution}) \]
-
Sam believes (-4, -7) is a solution: \[ 1.5(-4) - 2(-7) = -6 + 14 = 8 \quad (\text{this is a solution}) \]
-
Peter believes (-4, 7) is a solution: \[ 1.5(-4) - 2(7) = -6 - 14 = -20 \quad (\text{not a solution}) \]
Conclusion: Only Sam's belief that \((-4, -7)\) is a solution is correct, as it satisfies the equation \(1.5x - 2y = 8\).