Question

What is the slope of the line that passes through the pair of points(-5/3) and (-2, 9/)?

Answer 1

Use the slope formula:
\[\LARGE m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\]

Answer 2

Then after the slope, use the point-slope formula:
\[\LARGE y-y_{1}=m(x-x_{1})\]

Answer 3

Hey, Frinchie, if you meant the points (-5,3) and (-2,9), you could label \[x _{1}=-5,y _{1}=3,\]
and so on. Doesn't matter which of the two points you think of as #1.

Answer 4

I can't figure out the slope formula I can't find the way to subtract the fractions from the other number(s)

Answer 5

OK. First of all, our friend Luigi is right on target in providing the slope formula:
\[m=\frac{ y _{2}-y _{1} }{ x _{2}-x _{1} }\]

Answer 6

If, as I suggested earlier, \[x _{1}=-5,y _{1}=3,x _{2}=-2,andy _{2}=9,\]

Answer 7

all you need to do next is to substitute those values into Luigi's slope formula. Would you please try doing that?

Answer 8

so, 6 over -7???

Answer 9

Please double check your work. I got 6 over 3.

Answer 10

Please pay special attention when you subtract negative numbers.

Answer 11

We agree on the 6 in the numerator.
As for the denominator, since \[x _{2}=-2 and x _{1}=-5, we need (-2)-(-5).\]

What does that come to?

Answer 12

I re-did my work and yeah it =6 over 3, so that would mean that we need to grab the next equation that Luigi gave us?

Answer 13

Yes. But first, please reduce 6/3. That's your slope. In simplest form, your slope has what value?

Answer 14

So I reduced it to 1 over 2, or 1/2

Answer 15

As I see it, Frinchie, 6/3 reduces to 2/1. What do you think?

Answer 16

\[\frac{ 6 }{ 3 }=\frac{ 2*3 }{ 1*3 }=?\]

Answer 17

That looks right,

Answer 18

OK. Luigi's second equation is the point-slope formula for a straight line, used when we know one point on the line in question and also know the slope of the line. We're in that situation now. You may pick EITHER of the 2 given points, as well as use the slope m=2 that we just got.
Which point would you like to use? Really, it doesn't matter which one you choose.

Answer 19

Will 3 work?

Answer 20

OK. Here's that formula: \[y-y _{1}=m(x-x _{1}).\]

Answer 21

We found that the slope, m, is 2, didn't we?

Answer 22

Since you mention "3" I'm assuming that you chose to use the first point: (-5,3). That's just fine. You could have used the other point and still arrived at the correct equation of the line in question.

Answer 23

So, Frinchie, your slope is m=2, your \[x _{1}=-5,y _{1}=3.\]

Answer 24

Go ahead and substitute those values into Luigi's "point-slope form".

Answer 25

So we currently have Y-3=2(X+5) as are equation?

Answer 26

Yes, that's perfect. Excellent!
Let's summarize what you've done. You've taken the two given points and from them you've found the slope of the line, which is 2.

Answer 27

You then substituted the appropriate coordinates from the first point into that point-slope equation, along with the slope m=2.
You've ended up with the equation of the line in question.
You could either stop there, or

Answer 28

you could add 3 to both sides of the equation to solve it for y.

Answer 29

We can stop there, can I ask one more question?

Answer 30

Of course, please go ahead!

Answer 31

Write y=(-3 over 4)x=3

Answer 32

x+3*

Answer 33

Let me give you my interpretation: Did you mean:\[y=\frac{ 3 }{ 4 }x+3?\]

Answer 34

Oops..I missed the negative sign.

Answer 35

yup

Answer 36

What aspect of this equation would you like to discuss?

Answer 37

How to do this I havn't really understood this whole concept

Answer 38

Mind saying what it is that you would like to "do"?
What you have there is just the equation of a straight line in slope-intercept form.

Answer 39

Note that this form is different from the point-slope form Luigi and we used before.

Answer 40

Nevermind I figured it out thanks for the help!!!

Answer 41

Very happy to work with you. Encourage you to come back to OpenStudy with further questions. Just out of curiosity, where are you located? I'm in S. California.

Answer 42

Alpine Utah

Answer 43

Cool. What a beautiful state! All the best to you, and Happy New Year!

Answer 44

Happy new year to you aswell

Answer 45

So long for now! over and out.