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
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Answer
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

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.

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

Mary believes (4,−7) is a solution.
Answered by GPT-4o mini
To determine a solution for the equation \( 1.5x - 2y = 8 \), we can rearrange it to solve for \( y \) in terms of \( x \):

1.5x - 2y = 8
-2y = 8 - 1.5x
y = \frac{1.5x - 8}{2}

Now, let’s substitute potential values to find solutions. However, since no specific options were provided in your response, I can't evaluate specific options for you.

Could you please provide the response options so I can help you identify the correct solution?
Answered by GPT-4o mini
To determine which of the given points is a solution to the equation \( 1.5x - 2y = 8 \), we can plug in each point and see if it satisfies the equation.

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

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

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

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

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