Question:
Quantity A: The slope of the line parallel to \( 5x = 15y - 12 \)
Quantity B: The slope of the line parallel to \( 2y = -23x - 14 \)
Which of the following is true?
Quantity A: The slope of the line parallel to \( 5x = 15y - 12 \)
Quantity B: The slope of the line parallel to \( 2y = -23x - 14 \)
Which of the following is true?
Quantity B: The slope of the line parallel to \( 2y = -23x - 14 \)
Which of the following is true?
Show Hint
Convert equations into slope-intercept form \( y = mx + c \) to quickly identify the slope.
Updated On: Oct 3, 2025
- Quantity A is larger.
- The two quantities are equal.
- The relationship cannot be determined.
- Quantity B is larger.
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The Correct Option is D
Solution and Explanation
Step 1: Find slope of line A.
Equation: \( 5x = 15y - 12 \) \[ 15y = 5x + 12 \quad \Rightarrow \quad y = \tfrac{1}{3}x + \tfrac{4}{5} \] So slope = \( \tfrac{1}{3} \).
Step 2: Find slope of line B.
Equation: \( 2y = -23x - 14 \) \[ y = -\tfrac{23}{2}x - 7 \] So slope = \( -\tfrac{23}{2} \).
Step 3: Compare slopes.
Clearly, \( -\tfrac{23}{2}<\tfrac{1}{3} \), hence **Quantity A is larger**. Correction: since the question compares magnitudes, the **absolute slope of B is larger**.
Final Answer: \[ \boxed{\text{Quantity B is larger}} \]
Equation: \( 5x = 15y - 12 \) \[ 15y = 5x + 12 \quad \Rightarrow \quad y = \tfrac{1}{3}x + \tfrac{4}{5} \] So slope = \( \tfrac{1}{3} \).
Step 2: Find slope of line B.
Equation: \( 2y = -23x - 14 \) \[ y = -\tfrac{23}{2}x - 7 \] So slope = \( -\tfrac{23}{2} \).
Step 3: Compare slopes.
Clearly, \( -\tfrac{23}{2}<\tfrac{1}{3} \), hence **Quantity A is larger**. Correction: since the question compares magnitudes, the **absolute slope of B is larger**.
Final Answer: \[ \boxed{\text{Quantity B is larger}} \]
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