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 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. close. any line with a negative slope will be perpendicular to a line with a positive slope. 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. nice job, eddie. that is a good way to explain it.

Explanation:

The slope of a line perpendicular to a line with slope $m$ is the negative - reciprocal of $m$. If $m = 3$, the negative - reciprocal is $-\frac{1}{3}$. Eddie's statement is incorrect.

Answer:

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 $-\frac{1}{3}$.