Question

question 4
eddie wanted to clarify his understanding of the differences between parallel and perpendicular lines on a graph. which statement is the correct interpretation of the differences between parallel and perpendicular lines?
the slopes of parallel lines are negative reciprocals of each other, and the slopes of perpendicular lines are the same.
parallel lines have the same slope, but perpendicular lines have the same slope except one is positive and one is negative.
parallel lines have the same slope; however, the slopes of perpendicular lines are negative reciprocals of each other.
parallel lines have a slope that is undefined, which makes them vertical lines, and perpendicular lines have a slope of zero, which makes them horizontal lines

Explanation:

To determine the correct statement about parallel and perpendicular lines:

• Recall the slope properties: Parallel lines have equal slopes. Perpendicular lines (non - vertical/non - horizontal) have slopes that are negative reciprocals (e.g., if one slope is \(m\), the other is \(-\frac{1}{m}\)).
• Analyze each option:
• First option: Incorrect, as perpendicular slopes are negative reciprocals, not same, and parallel slopes are not negative reciprocals.
• Second option: Incorrect, perpendicular slopes are negative reciprocals, not same with sign change.
• Third option: Correct. Parallel lines have the same slope. For perpendicular lines (excluding vertical/horizontal edge cases), slopes are negative reciprocals (e.g., \(m\) and \(-\frac{1}{m}\)).
• Fourth option: Incorrect, vertical lines have undefined slope, horizontal have 0, but this misrepresents perpendicularity (vertical and horizontal are perpendicular, but the option’s wording is confusing and incorrect for general lines).

Answer:

The third option (Parallel lines have the same slope, but perpendicular lines have slopes that are negative reciprocals of each other (the option text: "Parallel lines have the same slope; however, the slopes of perpendicular lines are negative reciprocals of each other."))