Question

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.

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

Peter 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 can substitute each pair of coordinates into the equation and check if the equation holds true.

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

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

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

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

**Conclusion**: The only correct solution is given by Sam: \((-4, -7)\).