Question

Lines k and p are perpendicular, neither is vertical and p passes through the origin. Which is greater?

A. The product of the slopes of lines k and p

B. The product of the y-intercepts of lines k and p

Answer 1

Perpendicular lines have opposite reciprocal slope. If we say the slope of line k is \(m\), then the slope of line p would have to be \((-\frac{ 1 }{ m})\).

What's
\[m * \frac{ -1 }{ m }\]

Answer 2

-1

Answer 3

right, so we know the result for A is -1.

Answer 4

wait why is it -1? how did u get that?

Answer 5

That's what we just did. I was just restating the result

Answer 6

I don't understand how we got that....

Answer 7

we got -1 from the multiplication you did.
m*(-1/m)

Answer 8

yea but where and how did u get that?

Answer 9

Perpendicular lines have opposite reciprocal slope. If we say the slope of line k is m, then the slope of line p would have to be (−1/m).

Answer 10

oh okay. but for the problem itself it didn't give the slope

Answer 11

we don't need to know the slope. Knowing the relationship between the two lines is enough because they don't ask for the actual slopes. They only ask for their products

Answer 12

hmmmm ok

Answer 13

so whats next?

Answer 14

now we look at B. It says line p passes through the origin, so that means its y-intercept is 0.
We don't need to know the y-intercept of line k because any number multiplied by 0, is 0.
That means the result for B is 0.

Answer 15

Okay so i get B but for A how do we know it's a positive slope and not a negative one?

Answer 16

it doesn't matter. If we said k had a slope of -m, then the opposite reciprocal of that would be 1/m. When you multiply you'd still get -1

Answer 17

OHHHHHHHHHHHHHHHHHHHHHHHHHHHH because they're perpendicular they will automatically be a negative for the product!!!!!!!!!!!!!!

Answer 18

<333333 thank you

Answer 19

right :)

Answer 20

you're welcome

Answer 21

so B is greater

Answer 22

yes

Answer 23

thank u =)