Question

The math teacher asked his students to determine a solution for 1.5x−2y=8 . Which solution below is the correct one?(1 point) Responses 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. Sam believes left parenthesis negative 4 comma negative 7 right parenthesis is a solution. Fiona believes (4,7) is a solution.

Answer 1

To determine which of the given points is a solution to the equation \(1.5x - 2y = 8\), we will substitute each point into the equation and see if it satisfies it.

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

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

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

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

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

**Answer: Sam believes (-4, -7) is a solution.**