To determine whether the lines represented by the equations \( y = \frac{23}{2} x - \frac{285}{100} \) and \( y = 23x + 60 \) are parallel or perpendicular, we first need to identify their slopes.
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Finding the slope of the first line: The equation given is \( y = \frac{23}{2} x - \frac{285}{100} \).
- The slope (m₁) of this line is \( \frac{23}{2} \).
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Finding the slope of the second line: The equation is \( y = 23x + 60 \).
- The slope (m₂) of this line is \( 23 \).
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Comparing the slopes: Because the two slopes are compared, we check:
- For the lines to be parallel, their slopes must be equal, which means \( m₁ = m₂ \).
- For the lines to be perpendicular, the product of their slopes must equal \(-1\), which means \( m₁ \cdot m₂ = -1 \).
Let's compute the product of the slopes: \[ \frac{23}{2} \cdot 23 = \frac{23 \cdot 23}{2} = \frac{529}{2} \]
Since \( \frac{529}{2} \) is not equal to \(-1\), the lines are not perpendicular.
Next, let's compare the slopes: \[ \frac{23}{2} \text{ (which is 11.5) is not equal to } 23. \]
Since \( \frac{23}{2} \) is not equal to \( 23 \), the lines are not parallel.
Conclusion: The lines are neither parallel nor perpendicular.