Question

A line contains the points (3, -4) and (5, 2). Another line graphed in the same coordinate plane contains the points (0, -2) and (6, -4). Based on the slopes of these lines are they parallel, perpendicular or neither?

Answer 1

can someone please help ?

Answer 2

OK, did you find the equations of the lines?

Answer 3

i think so

Answer 4

What did you get?

Answer 5

the first one i got 1
and the second set of numbers i got -10 over 6

Answer 6

How did you get those? Something is not right there and I want to see if we can find out where the mistake is.

Answer 7

i did 2-3 over 5-4 for the first set and -4-6 over 6-0 . the first set gave me -1 over 1 which goes to 1 and the second set i got -10 over 6

Answer 8

Ah, you confused which values go where. OK. Let me show you something about that.

Answer 9

Usually you go through a section where you have the slope formula:
\[m=\frac{\Delta y}{\Delta x}\implies m=\frac{y_1-y_2}{x_1-x_2}\]
It really does not matter which point you choose as \((x_1,y_1)\) or \((x_2,y_2)\), but once one is chosen as being first, you must use the numbers from it in the first spots.
So lets take your points, \((3,-4)\) and \((5,2)\). If I say \((5,2)\) is the first one, then I must use this to get the slope:\[m=\frac{2-(-4)}{5-3}\]

Answer 10

have sent me something else

Answer 11

oh okay thank you

Answer 12

Yah, I was writing it up in an editor to make sure I for it all right. Causes a delay, but helps me make sure I get you good, clear info.

Answer 13

oh okay

Answer 14

would i do the same for the second set of numbers

Answer 15

Yes.

Answer 16

Once you have the two m values, let me know what you got.

Answer 17

i got the first m value is 3 and the second m value is -1

Answer 18

The first is 3. But check that second one. What did numbers did you put where in the slope formula?

Answer 19

-4 -2 over 6-0

Answer 20

AH! -4 - (-2)

Answer 21

Sign is like pants! Be careful not to drop them in the wrong place or it can be embarrassing. Hehe.

Answer 22

\[\frac{-4-(-2)}{6-0}\implies \frac{-4+2}{6}\]
That help?

Answer 23

would m be one third

Answer 24

Negative one third.

Answer 25

oh okay

Answer 26

That means you have \(m_1=3\) and \(m_2=-\frac{1}{3}\)

To be honest, slope is one of the ones I regularly make mistakes on. Because the y is on top and I keep wanting to put the x there. It means I have to be very careful when I do slopes!

Now, do you know the rules for parallel, perpendicular, and other lines as it relates to slope? The value of \(m_1\) and \(m_2\) tells you about the relationship of the lines.

Answer 27

it wouldn't be paralleled or perpendicular cause they don't equal the same or would they intersect

Answer 28

Well, they are either parallel or they intersect. How would you tell if they were parallel?

Answer 29

Three choices for two lines:
Parallel
Intersect, but not at right angles
Intersect at right angles, AKA Perpendicular

Answer 30

if they were parallel then they wouldn't intersect

Answer 31

Yes, but do you know what that would mean in terms of the slope? That is the final part of this question, what the slope means.
They are either Parallel
OR
They do Intersect, but not at right angles
OR
They do Intersect at right angles, AKA Perpendicular

It must be one of those three and the slope tells us which. Do you know how or do you need help with that part?

Answer 32

do you mind helping me with that part also

Answer 33

It is no problem!

These are the three choices, basically. Agreed?

Answer 34

yes

Answer 35

In Parallel, the slope is the same!