Pregunta
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Find the slopes of the lines and defined by the two given points. Then determine whether and are parallel, perpendicular, or neither.
and
and
Part:
The slope of is 3

Ask by Floyd Valdez. in the United States
Jan 27,2025

Solución de inteligencia artificial de Upstudy

Respuesta verificada por el tutor

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The slope of is and the slope of is . The lines are neither parallel nor perpendicular.

Solución

Let’s determine the slopes of lines and based on the given points and then analyze their relationship.

1. Calculating the Slope of

Given Points for : and .
The formula for the slope ( ) between two points and is:
Applying the formula:
Slope of :
Note: It appears there was a miscalculation in your initial assessment stating the slope of is 3. The correct slope is .

2. Calculating the Slope of

Given Points for : and .
Applying the slope formula:
Slope of :

3. Analyzing the Relationship Between and

  • Parallel Lines: Two lines are parallel if their slopes are equal.
    Conclusion: and are not parallel.
  • Perpendicular Lines: Two lines are perpendicular if the product of their slopes is .
    Conclusion: and are not perpendicular.
  • Neither Parallel Nor Perpendicular: Since neither condition above is met.
    Final Conclusion: and are neither parallel nor perpendicular.

Summary

  • Slope of :
  • Slope of :
  • Relationship: Neither parallel nor perpendicular.

Respondido por UpStudy AI y revisado por un tutor profesional

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The Deep Dive

To find the slope of line defined by the points and , we use the formula for slope:
Substituting in the values:
So, the slope of line is , not 3! Now for line defined by points and :
Now, we check if the lines are parallel, perpendicular, or neither. Lines are parallel if their slopes are equal and perpendicular if the product of their slopes equals -1. Here, and . The product is:
Since the product is not -1, the lines and are neither parallel nor perpendicular.

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