Question

Make a conjecture about how these slopes are related. Verify by calculating the slopes by hand. (Diagram being attached.)

Answer 1

First, what are the slopes of the two lines (put in fraction form)?

Answer 2

that's part of the problem.... i can't figure it out.

Answer 3

look at the little brown triangles. They show the change in y and the change in x for each line. the slope is the change in y divided by the change in x

Answer 4

okay...so what do i do with them?

Answer 5

what did you get?

Answer 6

nothing....

Answer 7

at point P , the triangle shows you how far to move over and up to stay on the line
how far over (change in x) does it show?
how far up? (change in y) ?
now find change in y divided by change in x

Answer 8

okay so PQ = \[\left(\begin{matrix}1.67 \\ 1\end{matrix}\right)\] and RQ = \[\left(\begin{matrix}-0.6 \\ \end{matrix}\right)\]

Answer 9

(-0.6 over 1 I mean...)

Answer 10

yes. but 1.67 divided by 1 is just 1.67
same for the other slope: -0.6

This question wants you to notice something interesting: these two lines form a ninety degree angle (see the little box where they meet. that means a right angle)

multiply the two slopes, what do you get?

Answer 11

-1.002

Answer 12

almost -1. If 1.67 is rounded from 1 and 2/3 or 5/3
and -0.6 is written as -6/10 or -3/5
we would get
\[ \frac{5}{3}\cdot \frac{-3}{5} = -1 \]

so to answer this question
Make a conjecture about how these slopes are related.

make the "guess" (conjecture is a fancy word for guess) that when you multiply the slopes of two lines that form a right angle, you get -1.

then do 1.67* -0.6= -1.002 to show the conjecture might be true (depends on how accurate the 1.67 slope is)