Question

It's in the photo, it's a bit to hard to type out.

Answer 1

Perpendicular lines have slopes that are negative reciprocals.

If two perpendicular lines have slopes m1 and m2, then we have the following equation:

`m_1=-(1)/(m_2)`

Then, we can analyze each pair.

a) In this case, both lines have the same slope (m = 1/5). They are parallel, not perpendicular.

b) In this case, the slopes are different. They are reciprocals (m1 = 1/m2), but they are not negative reciprocals, so they are not perpendicular.

c) In this case the slopes are the negative of each other (2/3 and -2/3), but they are not negative reciprocals. Then, they are not perpendicular.

d) In this case, the slopes are negative reciprocals:

`-(1)/(m_2)=-(1)/(-(3)/(2))=(1)/((3)/(2))=(2)/(3)=m_1`

Then, this lines are perpendicular.

Answer: Option d.