Question

eddie was helping explain the concept of parallel and perpendicular lines to another classmate. he said \if a line has a slope of 3, a line perpendicular would have a slope of -3.\ his teacher overhears his explanation. which of the following statements might eddie’s teacher make to eddie and his classmate?
\close. a line perpendicular to a line with a positive slope will have a negative slope, however the slope will be the negative reciprocal. in other words, a line perpendicular to a line with a slope of 3 will have a slope of -⅓.\
\close. any line with a negative slope will be perpendicular to a line with a positive slope.\

ice job, eddie. that is a good way to explain it.\
\close, a line perpendicular to another line will have a reciprocal slope. in other words, a line perpendicular to a line with a slope of 3 will have a slope of ⅓.\

Explanation:

Step1: Recall the rule for perpendicular slopes

The slope of a line perpendicular to a line with slope \( m \) is the negative reciprocal, i.e., \( -\frac{1}{m} \). For \( m = 3 \), the perpendicular slope should be \( -\frac{1}{3} \), not \( -3 \).

Step2: Analyze each option

• First option: States the correct rule (negative reciprocal) and calculates \( -\frac{1}{3} \) for slope 3. This is correct.
• Second option: Says "any line with a negative slope" is perpendicular to positive slope, which is wrong (needs to be negative reciprocal, not just negative).
• Third option: Is a praise, not a correction.
• Fourth option: Claims reciprocal (positive \( \frac{1}{3} \)) instead of negative reciprocal, which is wrong.

Answer:

The first option (the one stating "Close. A line perpendicular to a line with a positive slope will have a negative slope, however the slope will be the negative reciprocal. In other words, a line perpendicular to a line with a slope of 3 will have a slope of \( -\frac{1}{3} \).")