Question

Dealing with parallel and perpendicular lines, and their slopes.

If two lines are parallel, and both of their slopes are 1.5, then I need to know what the two slopes relationship is. I first thought it was that they are both the same.

On another question, I have two perpendicular lines. One line has a slope of -2/3, and the line it crosses over has a slope of 1.5. I need to know the relationship between the two slopes of these lines.

Please don't just give me an answer, I would appreciate it if you told me how to find the relationship between two slopes.

Answer 1

**I first thought it was that they are both the same.***
that sounds right. parallel lines have identical slopes

for perpendicular slopes, you have
\[ m_1= -\frac{2}{3} , m_2 = 1.5\]
if we write 1.5 as 3/2:
\[ m_1= -\frac{2}{3} , m_2 = \frac{3}{2}\]
do you see any "pattern" ?

Answer 2

Hm. Is it because they are both the same number, but one is negative? (on the perpendicular one)

Answer 3

2/3 and 3/2 are not the same number. But they are related

Answer 4

OH. Oh, I can see it now. (Haha, I was seeing them as the same number)
Are they related because they involve the same numbers?

Answer 5

one is the "flip" of the other. actually the negative "flip"
Of course, people don't say flip, they say "negative reciprocal"

if one slope is \(m_1\), the slope of its perpendicular is \( m_2= - \frac{1}{m_1} \)

Answer 6

example
\[ m_1= -\frac{2}{3} \\
m_2= - \frac{1}{-\frac{2}{3}} \\
m_2= - \frac{1\cdot -\frac{3}{2}}{-\frac{2}{3}\cdot -\frac{3}{2}}= -\frac{ -\frac{3}{2}}{1}= \frac{3}{2}\\
\]

Answer 7

(But I think it's easier to just "flip" -2/3 to -3/2 then negate it, to get 3/2)

Answer 8

Oh! I can understand it now. :D Thank you very much! <3